Probability

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #51

`A` & `B` are two mutually independent events. If `P(A) = 3/5` and `P(A \cap B) = 4/9`, then value of `P(B)` is -
(a) `5/9`, (b) `8/9`, (c) `5/27`, (d) `20/27`
Ans: (d) `20/27`
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Question No: #52

`A` & `B` are two mutually independent events. If `P(A) = 1/3` and `P(A \cap B) = 1/6`, then value of `P(A^c \cap B^c)` is -
(a) `1/6`, (b) `2/3`, (c) `1/3`, (d) `2/9`
Ans: (c) `1/3`
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Question No: #53

If `A` & `B` are two independent events and `P(A) = 0.3` , `P(B) = 0.4` then find `P(A \cup B)` & `P(B | A)`
Ans: `0.58`, `0.40`
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Question No: #54

A and B are two independent events such that `P(A)=1/2`, `P(B)=1/5`. Then value of `P(A | A\cupB)` is --
(a) `1/5`, (b) `2/5`, (c) `5/6`, (d) `5/7`
Ans: (c) `5/6`
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Question No: #55

`A` & `B` are two mutually independent events. If `P(\bar{A} \cap B) = 2/15` and `P(A \cap \bar{B}) = 1/6`, then find `P(B)`
Ans: `1/6` or `4/5`
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Question No: #56

If `P(A^c \cup B^c) = 5/6`, `P(A) = 1/2` and `P(\bar{B}) = 2/3`, then are `A` & `B` independent events?
Ans: Yes
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Question No: #57

If `P(A) = 1/4`, `P(B) = 1/3` and `P(A - B) = 1/6`, then are `A` & `B` mutually independent?
Ans: Yes
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Question No: #58

If `A` & `B` are mutually independent events and `P(A \cup B^c) = 0.8` and `P(A) = 0.3`. Find `P(B)`
Ans: `2/7`
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Question No: #59

If `P(A - B) = 1/3`, `P(A) = 1/2` and `P(B) = 1/3`, then find the probability of occurring exactly the event `B`.
Ans: `1/6`
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Question No: #60

Two events `A` & `B` are such that `P(A) = 1/3`, `P(B) = 3/4`. Find the probability of occurring only event `B` provided that `A` is not occurred.
Ans: Between `[5/8, 1]`
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