Question

Probability:
Conditionality Probability and Independent events.

(i)
Two events A and B are said to be independent if
(a) P(A ∪ B) = P(A) P(B)
(b) P(A ∩ B) = 0
(c) P(A ∩ B) = P(A) P(B)
(d) none of these




(ii)
If events A and B are independent, P(A) = 0.35, P(A ∪ B) = 0.60 then P(B) is
(a) 0.25
(b) 0
(c) 0.95
(d) none of these




(iii)
The probability of A, B and C solving a problem are
and respectively. Then the probability that the problem will be solved is
(a) 1/2
(b)3/4
(c) 1/4
(d) none of these




(iv)
A man is known to speak truth in 3 out of 4 times. He throws a dice and reports that it is a six. Then the probability that it is actually a six is
(a) 4/9
(b) 2/7
(c) 1/6
(d) 3/8




(v)
A pair of dice is thrown and it is known that the second dice always exhibits an odd number. Then the probability that the sum obtained on two dice is 7, is
(a) 1/6
(b) 5/6
(c)1/2
(d) none of these​

Answer 1

Answer:

A conditional probability can always be computed using the formula in the definition. Sometimes it can be computed by discarding part of the sample space. Two events A and B are independent if the probability P(A∩B) of their intersection A ∩ B is equal to the product P(A)·P(B) of their individual probabilities.