Probability Questions for SBI PO

Probability Questions for SBI PO

Probability Questions for SBI PO 2017 Exam

1. There are 27 cards having number 1 to 27. Two cards are picked at random one by one. What is the probability that sum of number on these 2 cards is odd? (SBI PO Prelim Exam 2017)
\(\left( a \right) \frac { 13}{ 27}\)
\(\left( b \right) \frac {8 }{ 13}\)
\(\left( c \right) \frac { 182}{ 729}\)
\(\left( d \right) \frac { 14}{ 27}\)
(e) None of these

Quantitative Aptitude

There are three bags A, B and C. In  each bag there are three types of colored balls Yellow, Green and Black. (SBI PO Main Exam 2017)

In bag A, no. of yellow colored balls are y and no. of green colored balls are g. Number of green colored balls are 4 more than the number of yellow colored balls. When one ball is picked at random then the probability of getting color ball is \(\frac { 5 }{ 13 } \). The value of y is \(18\frac { 2 }{ 11 } %\) less than g.

In bag b, number of yellow colored balls is \(22\frac { 2 }{ 9 } %\) more than that of bag A. If two balls are picked at random from bag B then the probability of getting both green color ball is  \(\frac { 4 }{ 7 } \). Total number of ball in bag B is 75.

In bag C, the ratio of number of green colored balls and number of black colored balls is 7 : 5. Total number of green and black colored balls is 36. If one ball is picked at random then the probability of getting one yellow ball is \(\frac { 7 }{ 13} \)

2. If x number of yellow balls from bag B are taken and placed into bag A and 20 % of black balls from the bag A are taken and placed int o in bag B. If we pick one ball from bag B then the probability that the ball is of balck color is \(\frac { 11 }{ 26} \). Then find the value of x?
(a) 5
(b) 6
(c) 3
(d) 2
(e) None of these

3. If one ball picked at random from each of the bag A and bag B then find the probability that both of the balls are of the same color?
\(\left( a \right) \frac { 21\times 47 }{ 65\times 75 } \)
\(\left( b \right) \frac { 22\times 43}{ 65\times 75 } \)
\(\left( c \right) \frac { 11\times 17}{ 65\times 75 } \)
(d) Can’t be determined
(e) None of these

4. Difference between the number of green balls in bag A and bag C is how much percent more/less than the sum of the number of black balls in bag A and bag C together?
(a) 100%
(b) 95%
(c) 67.5%
(d) 102.5%
(e) None of these

Probability Questions for SBI PO 2017 Answers

1. (d)
Odd sum is there when one card drawn is odd and another even.
⇒ Required probability
\(=\left( \frac { 13 }{ 27 } \times \frac { 14 }{ 26 } \right) \left( \frac { 14 }{ 27 } \times \frac { 13 }{ 26 } \right) =\frac { 14 }{ 27 } \)

2. (d)
After replacement →
Yellow no. of balls in bag B = 22 – x
Black no. of balls in bag B = 28 + 5 = 33
Green no. of balls in bag B = 25
Then,
\(\frac { 33 } { 22 \therefore x + 33 + 25 } = \frac { 11 } { 26 }\)
\(\frac { 33 } { 80 – x } = \frac { 11 } { 26 }\)
78 = 80 – x
x = 2

3. (e)
Required probability
\(= \frac { 18 } { 65 } \times \frac { 22 } { 75 } = \frac { 22 } { 65 } \times \frac { 25 } { 75 } = \frac { 25 } { 65 } \times \frac { 28 } { 75 }\)
\(= \frac { 1646 } { 65 \times 75 }\)

4. (c)
Required% \(= \frac { 40 \therefore 1 } { 40 } \times 100\)
\(= \frac { 39 } { 40 } \times 100\)
= 67.5%

Probability Questions for SBI PO 2013 Exam

1. A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow? (SBI PO 2013)
\(\left( a \right) \frac { 5 }{ 35 }\)
\(\left( b \right) \frac { 5 }{ 22 }\)
\(\left( c \right) \frac { 7 }{ 22 }\)
\(\left( d \right) \frac { 7 }{ 33 }\)
\(\left(e \right) \frac { 7 }{ 66 }\)

2. A die is thrown twice. What is the probability of getting a sum 7 from both the throws? (SBI PO 2013)
\(\left( a \right) \frac { 5 }{ 18 }\)
\(\left( b \right) \frac { 1 }{ 18 }\)
\(\left( c \right) \frac { 1 }{ 9 }\)
\(\left( d \right) \frac { 1 }{ 6 }\)
\(\left( e \right) \frac { 5 }{ 36 }\)

Probability Questions for SBI PO 2013 Answers

1. (c)
Blue balls = 7
None-ball out of two yellow
Yellow balls = 5
∴ Both balls are blue
Total balls = 12
∴P(bothblueballs)
\(=\frac { 7 }{ 12 } \times \frac { 6 }{ 11 } =\frac { 7 }{ 22 } \)

2. (d)
Total possible outcomes when A die is tin-own twice = 36
Outcome for getting a sum 7 from both throwns = 6{(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
∴ \(\quad \mathrm { P } ( \mathrm { E } ) = \frac { 6 } { 36 } = \frac { 1 } { 6 }\)

Probability Questions for SBI PO 2011 Exam

1. Out of five girls and three boys, four children are to be randomly selected for a quiz contest. What is the probability that all the selected children are girls? (SBI Associates PO 2011)
\(\left( a \right) \frac { 1 }{ 14 }\)
\(\left( b \right) \frac { 1 }{ 7 }\)
\(\left( c \right) \frac { 5 }{ 17 }\)
\(\left( d \right) \frac { 2 }{ 17 }\)
(e) None of these

Probability Questions for SBI PO 2011 Answer

1. (a)
Total number of ways of selecting 4 children out of 8
\(= ^ { 8 } \mathrm { C } _ { 4 } = \frac { 8 \times 7 \times 6 \times 5 } { 1 \times 2 \times 3 \times 4 } = 70\)
Number of ways of selecting 4 girls out of 5 = ⁵C₄ = 5
Required probability
\(= \frac { 5 } { 70 } = \frac { 1 } { 14 }\)

Probability Questions for SBI PO 2010 Exam

Study the given information carefully and answer the questions that follow :
Anurn contains 6 red, 4 blue, 2 green and 3 yellow marbles. (SBI Rural Bus. PO 2010)

1. If four marbles are picked at random, what is the probability that at least one is blue?
\(\left( a \right) \frac { 4 }{ 15 }\)
\(\left( b \right) \frac { 69 }{ 91 }\)
\(\left( c \right) \frac { 11 }{ 15 }\)
\(\left( d \right) \frac { 22 }{ 91 }\)
(e) None of these

2. If two marbles are picked at random, what is the probability that both are red?
\(\left( a \right) \frac { 1 }{ 6 }\)
\(\left( b \right) \frac { 1 }{ 3 }\)
\(\left( c \right) \frac { 2 }{ 15 }\)
\(\left( d \right) \frac { 2 }{ 5 }\)
(e) None of these

3. If three marbles are picked at random, what is the probability that two are blue and one is yellow?
\(\left( a \right) \frac { 3 }{ 31 }\)
\(\left( b \right) \frac { 1 }{ 5 }\)
\(\left( c \right) \frac { 18 }{ 455 }\)
\(\left( d \right) \frac { 7 }{ 15 }\)
(e) None of these

4. If four marbles are picked at random, what is the probability that one is green, two are blue and one is red?
\(\left( a \right) \frac { 24 }{ 455 }\)
\(\left( b \right) \frac { 13 }{ 35 }\)
\(\left( c \right) \frac { 11 }{ 15 }\)
\(\left( d \right) \frac { 1 }{ 3 }\)
(e) None of these

5. If two marbles are picked at random, what is the probability that either both are green or both are yellow?
\(\left( a \right) \frac { 5}{ 91 }\)
\(\left( b \right) \frac { 1 }{ 35 }\)
\(\left( c \right) \frac { 1 }{ 3 }\)
\(\left( d \right) \frac { 4 }{ 105 }\)
(e) None of these

A basket contains 4 red, 5 blue and 3 green marbles. (SBI Associates Bank PO 2010)
6. If three marbles are picked at random, what is the probability that either all are green or all are red ?
\(\left( a \right) \frac { 7 }{ 44 }\)
\(\left( b \right) \frac { 7 }{ 12 }\)
\(\left( c \right) \frac { 5 }{ 12 }\)
\(\left( d \right) \frac { 1 }{ 44 }\)
(e) None of these

7. If two marbles are picked at random, What is the probability that both are red ?
\(\left( a \right) \frac { 3 }{ 7 }\)
\(\left( b \right) \frac { 1 }{ 2 }\)
\(\left( c \right) \frac { 2 }{ 11 }\)
\(\left( d \right) \frac { 1 }{ 6 }\)
(d) None of these

8. If three marbles are picked at random, What is the probability that at least one is blue?
\(\left( a \right) \frac { 7 }{ 12 }\)
\(\left( b\right) \frac { 37 }{ 44 }\)
\(\left( c \right) \frac { 5 }{ 12 }\)
\(\left( d \right) \frac { 7 }{ 44 }\)
(e) None of these

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done if: (SBI Associates Bank PO 2010)
9. The committee should have all 4 professors and 1 research associate or all 3 trainees and 2 professors ?
(a) 12
(b) 13
(c) 24
(d) 52
(e) None of these

10. The committee should have 2 trainees and 3 research associates ?
(a) 15
(b) 45
(c) 60
(d) 9
(e) None of these

Probability Questions for SBI PO 2010 Answers

1. (b)
Number of way \(\frac { 5.72 } { 3 }\) lakh of selecting 4 marbles out of 15 marbles
\(= ^ { 15 } \mathrm { C } _ { 4 } = \frac { 15 \times 14 \times 13 \times 12 } { 4 \times 3 \times 2 \times 1 } = 1365]\)
Number of ways of selecting 4 marbles when no one is blue
\(= ^ { 11 } \mathrm { C } _ { 4 } = \frac { 11 \times 10 \times 9 \times 8 } { 4 \times 3 \times 2 \times 1 } = 330\)
Probability of getting 4 marble (when no one is blue)
= \frac { 330 } { 1365 } = \frac { 22 } { 91 }
\(Probability that at least one is blue \)
\(= 1 – \frac { 22 } { 91 } = \frac { 69 } { 91 }\)

2. (e)
Number of ways of selecting 2 red marbles from 6 red marbles = ⁶C₂= 15
Number of ways of selecting 2 marbles from urn = ¹⁵C₂=105
Required Probability
\(= \frac { 15 } { 105 } = \frac { 1 } { 7 }\)

3. (c)
Number of ways of selecting 2 blue and one yellow marble = ⁴C₂ × ³C₁= 6 × 3 = 18
Number of ways of selecting 3 marble from urn = ¹⁵C₃ = 455
Required Probability
\(= \frac { 18 } { 455 }\)

4. (a)
Number of ways of selecting one green, two blue and one red marble = ²C₁ × ⁴C₂ × ⁶C₁.
= 2 × 6 × 6 = 72
Number of ways of selecting 4 marbles from urn = ¹⁵C₄
\(= \frac { 12 \times 13 \times 14 \times 15 } { 4 \times 3 \times 2 \times 1 } = 1365\)
Required Probability
\(= \frac { 72 } { 1365 } = \frac { 24 } { 455 }\)

5. (d)
Number of ways of selecting either two green marbles or two yellow marbles = ²C₂ + ³C₂ = 1 + 3 = 4
Number of ways of selecting 2 marbles = ¹⁵C₂ = 105
Required Probability
\(= \frac { 4 } { 105 }\)

6. (d)
Total possible outcomes = Number of ways of picking
3 marbles out of 12 marbles = n(S)
\(= 12 _ { \mathrm { c3 } } \frac { 12 \times 11 \times 10 } { 1 \times 2 \times 3 } = 220\)
Favourable number of cases = n(E)
= ³C₃ + ⁴C₃
= 1 + 4=5
∴ Required probability
\(= \frac { \mathrm { n } ( \mathrm { E } ) } { \mathrm { n } ( \mathrm { S } ) } = \frac { 5 } { 220 } = \frac { 1 } { 44 }\)

7. (e)
Total possible outcomes
\(= \mathrm { n } ( \mathrm { S } ) = ^ { 12 } \mathrm { C } _ { 2 } = \frac { 12 \times 11 } { 1 \times 2 } = 66\)
Favourable number of cases = n(E)
\(= ^ { 4 } \mathrm { C } _ { 2 } = \frac { 4 \times 3 } { 1 \times 2 } = 6\)
∴ Required probability
\(= \frac { \mathrm { n } ( \mathrm { E } ) } { \mathrm { n } ( \mathrm { S } ) } = \frac { 6 } { 66 } = \frac { 1 } { 11 }\)

8. (b)
Total possible outcomes = n(S) = ¹²C₃ = 220
Favourable number of ways of picking 3 marbles (none is blue) out of 7 marbles
\(= ^ { 7 } \mathrm { C } _ { 3 } = \frac { 7 \times 6 \times 5 } { 1 \times 2 \times 3 } = 35\)
∴ Required probability
\(= \left( 1 – \frac { 35 } { 220 } \right) = 1 – \frac { 7 } { 44 } = \frac { 37 } { 44 }\)

9. (a)
Number of combinations
= (⁴C₄ × ⁶C₁ + ³C₃ × ⁴C₂) = 1 × 6 + 1 × 6 = 12

10. (c)
Number of combinations
= Selecting 2 trainees out of 3 and selecting 3 research associates out of 6 = ³C₂ × ⁶C₃
\(= 3 \times \frac { 6 \times 5 \times 4 } { 1 \times 2 \times 3 } = 60\)