Please help D Suppose that I flip a penny and a nickel each

Please help :D

Suppose that I flip a penny and a nickel, each coin is equally likely to come up heads and tails, and the two flips are independent What is the conditional probability that both coins come up heads, given that the penny came up heads? What is the conditional probability that both coins come up heads, given that a coin comes up heads?

Solution

Consider the table of possible results:

a)

In the two ways the penny came up heads, there is one case where both coins is heads.

Thus,

P(both are heads|penny is heads) = 1/2 OR 0.5 [ANSWER]

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b)

There are 3 results in which at least a coin came up heads.

Among which, only one had both heads,

Thus,

P(both heads|a coin is heads) = 1/3 or 0.33333333 [answer]

Penny	Nickel
H	H
H	T
T	H
T	T