Probability

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

Click on each question to see answer & solution.

Question No: #61

If `A` & `B` are two events such that `P(A) = 1/4`, `P(A | B) = 1/2` and `P(B | A) = 2/3` then value of `P(B)` is --
(a) `1/2`, (b) `1/6`, (c) `2/3`, (d) `1/3`
Ans: (d) `1/3`
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Question No: #62

If `P(A) = 1/4`, `P(A | B) = P(B | A) = 1/2`, then find `P(A^c | B^c)`
Ans: `5/6`
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Question No: #63

If `P(A | B) = 0.75`, `P(B | A) = 0.6` and `P(A) = 0.4`, then find `P(\bar{A} | \bar{B})`
Ans: `13/17`
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Question No: #64

If `P(A | B) = 0.8`. `P(B | A) = 0.6` & `P(A^c \cup B^c) = 0.7`; then find `P(A \cup B)`
Ans: `23/40`
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Question No: #65

If `P(A) = 1/3`, `P(A \cap B^c) = 1/4`; then value of `P(B | A)` is -
(a) `1/4`, (b) `1/3`, (c) `1/12`, (d) `3/4`

Question No: #66

Two events `A` & `B` are such that `P(A) = P(A | B) = 1/4`, `P(B | A) = 1/2`, then --
(a) `A` & `B` are independent, (b) `A` & `B` are not independent, (c) `P(A \cup B) = 0`, (d) None of these
Ans: (a) `A` & `B` are independent,
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Question No: #67

For any two events `A` & `B`, if `P(A) = 1/8`, `P(A | B) = 1/8` and `P(B | A) = 1/4`, then are these events mutually exclusive?

Question No: #68

`A` & `B` are two events such that `P(\bar{B}) = 1/2`, `P(A \cup B) = 5/6` and `P(A \cap B) = 1/3`, then the events `A` & `B` are -
(a) independent (b) dependent (c) mutually exclusive (d) none of these
Ans: (a) independent
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Question No: #69

If the events `A` & `B` are mutually independent, then prove that the events `A^c` & `B^c` are also mutually independent.
If the events `A^c` & `B^c` are mutually independent, then prove that the events `A` & `B` are also mutually independent.

Question No: #70

If `A` & `B` are mutually independent events, then prove that `P(A | B^c) = P(A)`