Probability

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

Click on each question to see answer & solution.

Question No: #71

For any two events `A` & `B` (where `P(B) \ne 0`), show that `P(A | \bar{B}) = P(A)`

Question No: #72

If `P(A) = a` and `P(B) = b`, then show that -
(i) `P(A | B) \le a/b`
(ii) `P(A | B) \gt (a+b-1)/b`

Question No: #73

If `A` & `B` are any two events of a random experiment, then prove that `P(\bar{A} | B) = 1 - P(A | B)`

Question No: #74

If `A` & ``B are mutually exclusive and `P(B) \ne 0` then `P(A | \bar{B})` is -
(a) `\frac{1}{P(B)}` (b) `\frac{1}{1 - P(B)}` (c) `\frac{P(A)}{P(B)}` (d) `\frac{P(A)}{1 - P(B)}`
Ans: (d) `\frac{P(A)}{1 - P(B)}`
SEE SOLUTION

Question No: #75

If `P(A | B) = P(A)`, then prove that `P(A^c | B) = P(A^c)`

Question No: #76

If `P(A | B) = 0.8`, `P(B | A) = 0.6` and `P(A^c \cup B^c) = 0.7`, then find `P(A | B^c)` & `P(A\cup B)`
Ans: 0.32, `23/40`
SEE SOLUTION

Question No: #77

If `P(A | B)=1`, then prove that `P(ABC)=P(BC)`

Question No: #78

The events `A` & `B` are mutually independent and `P(A), P(B) \gt 1/2`. `P(A \cap B^c) = 3/25` & `P(A^c \cap B) = 8/25`. Then find the value of `P(A)` & `P(B)`
Ans: `3/5, 4/5`
SEE SOLUTION

Question No: #79

If `A_1, A_2, \cdots, A_n` are mutually independent events and `P(A_i) = 1 - q_i` (`i = 1, 2, \cdots, n`), then prove that `P(A_1 \cup A_2 \cup \cdots \cup A_n) = 1 - q_1 q_2 \cdots q_n`

Question No: #80

If A & B are two independent events, then show that the probability of occurring at least one event is `1 - P(A^c)P(B^c)`