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If a student (represented by initials) was chosen at random, find P(HH|C).

If a student (represented by initials) was chosen at random, find P(HH|C).-example-1

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The conditional probability formula is given as


P(HH|C)=(P(HH\cap C))/(P(C))

where


P(HH\cap C)

denotes the probability of the intersection zone.

From the given picture, we can note that the number of elements in each of the above zones are:


\begin{gathered} n(HH\cap C)=4 \\ \text{and} \\ n(C)=10 \end{gathered}

Then, we have


P(HH|C)=(P(HH\cap C))/(P(C))=(4)/(10)

by symplifing this result, we have


P(HH|C)=(2)/(5)

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