Video: EG19M1-Statistics-Q01

If 𝑃(𝐴 ∩ 𝐡) = 2/5 and 𝑃(𝐴) = 4/5, find 𝑃(𝐡 | 𝐴).

01:20

Video Transcript

If the probability of 𝐴 and 𝐡 is two-fifths and the probability of 𝐴 is four-fifths, find the probability of 𝐡 given 𝐴.

The probability of 𝐡 given 𝐴 is a conditional probability. We find the probability of 𝐡 given 𝐴 by taking the probability of 𝐴 and 𝐡 and dividing it by the probability of 𝐴. We’re given the probability of 𝐴 and 𝐡 and the probability of 𝐴. So for our situation, the probability of 𝐡 given 𝐴 equals two-fifths over four-fifths, the probability of 𝐴 and 𝐡 over the probability of 𝐴.

Two-fifths divided by four-fifths equals two-fifths times five over four. The five in the numerator and the denominator cancel out. Two times one equals two. One times four equals four. Two-fourths can be reduced to one-half. And the probability of 𝐡 given 𝐴 is one-half.

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