The conditional probability of an event E, given the occurrence of the event F is given by

**A. ** P(E|F)=P(E∩F)P(F),P(F)<0
**B. ** P(E|F)=P(E∪F)P(F),P(F)≠0
**C. ** P(E | F) =P(E∩F)P(F), P(F)≠0
**D. ** P(E|F)=P(E∩F)P(E),P(F)≠0
**Answer : ****Option C**

**Explaination / Solution: **

The conditional probability of an event E, given the occurrence of the event F is given by :

The conditional probability of an event E, given the occurrence of the event F is given by :

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If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A|B)

**A. ** 0.68

**B. ** 0.64

**C. ** 0.66

**D. ** 0.62

**Answer : ****Option B**

**Explaination / Solution: **

We have ,

P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

We have ,

P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

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A dice is tossed once and even number has come up. The chance that it is either 2 or 4 is

**A. ** 2/ 6

**B. ** None of these

**C. ** 4/ 9

**D. ** 2/ 3

**Answer : ****Option D**

**Explaination / Solution: **

Total number of ways of getting even number is 3

Out of these 3 even number we have to get either 2 or 4 which can be done in 2 ways.

So required probability is 2/3

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The letters of the word ‘ ORIENTAL ‘ are arranged in all possible ways . The chance that the consonants and vowels occur alternately is

**A. ** 2/ 35

**B. ** None of these

**C. ** 1/35

**D. ** 1/70

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Let A and B be two independent events. The probability that both A and B occur is and the probability that neither A nor B occurs is . The respective probabilities of A and B are

**A. ** 12and16
**B. ** 1/3 and 1/4 or 1/4 and 1/3

**C. ** none of thse

**D. ** 16and12
**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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One ticket is selected at random from 100 tickets numbered 00, 01, 02…, 99. Suppose S and T are the sum and product of the digits of the number on the ticket, then the probability of getting S = 7 and T = 0 is

**A. ** 150
**B. ** 219
**C. ** 19100
**D. ** 14
**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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A cubical dice has 3 on three faces , 2 on two faces and 1 on the 6 face .It is tossed twice . The chance that both the tosses show an even number is

**A. ** none of these.

**B. ** 1/ 36

**C. ** 1/4

**D. ** 1/9

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Given that the events A and B are such that P(A) =, P (A ∪ B) = and P(B) = p. Find p if they independent.

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In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability . What is the probability that the student knows the answer given that he answered it correctly?

**A. ** 1113
**B. ** 1213
**C. ** 713
**D. ** 913
**Answer : ****Option B**

**Explaination / Solution: **

Let are events that the student knows the answer and the student guesses respectively.

Let are events that the student knows the answer and the student guesses respectively.

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A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)

**A. ** 1/5

**B. ** 1/2

**C. ** 1/3

**D. ** 2/3

**Answer : ****Option B**

**Explaination / Solution: **

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