Probability problems
- 1. The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of success of at least two.
Options- A. 1/4
- B. 1/2
- C. 1/6
- D. 1/3 Discuss
Correct Answer: 1/6
Explanation:
P(X) = , P(Y) = , P(Z) =
Required probability:
= [ P(A)P(B){1?P(C)} ] + [ {1?P(A)}P(B)P(C) ] + [ P(A)P(C){1?P(B)} ] + P(A)P(B)P(C)
=
= = =
- 2. I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?
Options- A. 1/999
- B. 1/1001
- C. 1/1000
- D. 4/1000 Discuss
Correct Answer: 1/1000
Explanation:
It is given that last three digits are randomly dialled. then each of the digit can be selected out of 10 digits in 10 ways.
Hence required probability =
= 1/1000
- 3. Out of 3 girls and 6 boys a group of three members is to be formed in such a way that at least one member is a girl. In how many different ways can it be done?
Options- A. 64
- B. 84
- C. 56
- D. 20 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 64
Explanation:
Total number of possible ways = 9C3 = 84 ways
Required atleast one girl in the group of three = total possible ways - ways in which none is girl
None of the members in the group is girl = 6C3 = 20
Therefore, number of ways that at least one member is a girl in the group of three
= 84 - 20
= 64 ways.
- 4. In a single throw with 2 dices, what is probability of neither getting an even number on one and nor a multiple of 3 on other?
Options- A. 11/36
- B. 25/36
- C. 5/6
- D. 1/6 Also asked in: Bank Exams, Bank PO, Bank Clerk
Correct Answer: 25/36
Explanation:
We first calculate the probability of getting an even number on one and a multiple of 3 on other,Here, n(s) = 6x6 = 36 and
E = (2,3) (2,6) (4,3) (4,6) (6,3) (6,6) (3,2) (3,4)(3,6) (6,2)(6,4)
n(E) = 11P(E) = 11/36Required probability = 1-11/36 = 25/36
- 5. If x is chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?
Options- A. 1/2
- B. 2/3
- C. 3/4
- D. 4/3 Discuss
Correct Answer: 2/3
Explanation:
S ={(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)} xy will be even when even x or y or both will be even. P(E)=n(E)n(S)=812 = 4/3 |
- 6. The probability that a number selected at random from the first 100 natural numbers is a composite number is ?
Options- A. 3/2
- B. 2/3
- C. 1/2
- D. 34/7 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 3/2
Explanation:
The number of exhaustive events = 100 C? = 100.
We have 25 primes from 1 to 100.
Number of favourable cases are 75.
Required probability = 75/50 = 3/2.
- 7. The probability that a bowler bowled a ball from a point will hit by the batsman is ¼. Three such balls are bowled simultaneously towards the batsman from that very point. What is the probability that the batsman will hit the ball ?
Options- A. 37/64
- B. 27/56
- C. 11/13
- D. 9/8 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 37/64
- 8. If an unbiased dice is rolled once, the odds in favour of getting a point which is multiple of 3 is:
Options- A. 1/2
- B. 2/1
- C. 1/3
- D. 3/1 Discuss
Correct Answer: 1/3
Explanation:
Total number =6
Getting a 'multiple of 3' = 2 . So, probability = 2/6 =1/3
- 9. Three dice are thrown together.Find the probability of getting a total of atleast 6.
Options- A. 103/216
- B. 103/108
- C. 103/36
- D. 36/103 Discuss
Correct Answer: 103/108
Explanation:
Total number of events=6 x 6 x 6=216
Let A be the event of getting a total of atleast 6 and B denoted event of getting a total of less than 6 i.e.,3,4,5.
So,B={(1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)}
Favourable number of cases=10
Therefore,P(B)=10/216
=> P(A) = 1 - P(B)
= 1 - (10/216) = 103/108
- 10. In a box, there are four marbles of white color and five marbles of black color. Two marbles are chosen randomly. What is the probability that both are of the same color?
Options- A. 2/9
- B. 5/9
- C. 4/9
- D. 0 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 4/9
Explanation:
Number of white marbles = 4
Number of Black marbles = 5
Total number of marbles = 9
Number of ways, two marbles picked randomly = 9C2
Now, the required probability of picked marbles are to be of same color = 4C2/9C2 + 5C2/9C2
= 1/6 + 5/18
= 4/9.
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