### Video Transcript

For two events π΄ and π΅, the
probability of π΅ prime equals 0.3 and the probability of π΄ given π΅ equals
0.3. Determine the probability of π΄
intersection π΅.

The first thing to note in this
question is weβre not given the probability of π΅, but instead weβre given the
probability of π΅ prime. This refers to the complement of
π΅, and itβs essentially the probability of π΅ not occurring. As we know all probabilities sum to
one, then this means that the probability of π΅ is equal to one subtract 0.3, and
thatβs 0.7. Weβre given the probability of π΄
given π΅ as 0.3, and we need to find the probability of π΄ intersection π΅.

We can use the formula for
conditional probability that tells us that the probability of π΄ given π΅ is equal
to the probability of π΄ intersection π΅ divided by the probability of π΅. As we want to find the probability
of π΄ intersection π΅, we can rearrange this formula to help us. Plugging the values into the
formula, the probability of π΄ given π΅ is 0.3 and the probability of π΅ is 0.7, so
we multiply those together, which gives us the answer that the probability of π΄
intersection π΅ is 0.21.