# Question Video: Applying the Multiplication Rule to Calculate Probabilities

For two events 𝐴 and 𝐵, P(𝐵′) = 0.3 and P(𝐴 ∣ 𝐵) = 0.3. Determine the probability of 𝐴 ∩ 𝐵

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### Video Transcript

For two events 𝐴 and 𝐵, the probability of 𝐵 prime equals 0.3 and the probability of 𝐴 given 𝐵 equals 0.3. Determine the probability of 𝐴 intersection 𝐵.

The first thing to note in this question is we’re not given the probability of 𝐵, but instead we’re given the probability of 𝐵 prime. This refers to the complement of 𝐵, and it’s essentially the probability of 𝐵 not occurring. As we know all probabilities sum to one, then this means that the probability of 𝐵 is equal to one subtract 0.3, and that’s 0.7. We’re given the probability of 𝐴 given 𝐵 as 0.3, and we need to find the probability of 𝐴 intersection 𝐵.

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