### Video Transcript

If the probability of π΄ and π΅ is two-fifths and the probability of π΄ is four-fifths, find the probability of π΅ given π΄.

The probability of π΅ given π΄ is a conditional probability. We find the probability of π΅ given π΄ by taking the probability of π΄ and π΅ and dividing it by the probability of π΄. Weβre given the probability of π΄ and π΅ and the probability of π΄. So for our situation, the probability of π΅ given π΄ equals two-fifths over four-fifths, the probability of π΄ and π΅ over the probability of π΄.

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 π΅ given π΄ is one-half.