Short Answer TypeA family has two children. What is the probability that both the children are boys given that at least one of them is a boy?
A couple has two children,
Find the probability that both children are males, if it is known that at least one of the children is male.
A couple has two children,
Find the probability that both children are females, if it is known that the elder child is a female.
Long Answer TypeAn electronic assembly consists of two subsystems, say A and B. From the previous testing procedures, the following probabilities are assumed to be known:
P( A fails) = 0.2
P(B fails alone) = 0.15
P(A and B fail) = 0.15
Evaluate the following probabilities:
(i) P( A fails 
) (ii) P(A fails alone)
S = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (1, H), (1, T), (2, H), (2, T), (4, H), (4, T), (5, H), (5, T)}
The outcomes of S are not equally likely. First 12 outcomes are equally likely and are such that the sum of their probabilities is 
So each of the first 12 outcomes has a probability equal to 
Remaining eight outcomes are equally likely and are such that the sum of their probabilities is 
So, each of these has a probability equal to 
Let E: 'the coin shows a tail'
and F: 'at least one die shows up a 3',
and 
Required probability = 
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