Video Transcript
For two events 𝐴 and 𝐵, the
probability of 𝐴 equals 0.3, the probability of 𝐵 equals 0.4, and the probability
of 𝐴 intersection 𝐵 equals 0.2. Work out the probability of 𝐴
given 𝐵. Work out the probability of 𝐵
given 𝐴.
In this question, we have two
events 𝐴 and 𝐵, and we’re given the probability of each of these events
happening. We’re also told the probability of
𝐴 intersection 𝐵, which is the probability that 𝐴 and 𝐵 both occur. The two questions that we’re asked
here both involve conditional probability.
In order to answer the first
question to work out the probability of 𝐴 given 𝐵, we can use the general formula
that the probability of 𝐴 given 𝐵 is equal to the probability of 𝐴 intersection
𝐵 divided by the probability of 𝐵. We can then plug in each of the
values into the formula to find the probability of 𝐴 given 𝐵. The probability of 𝐴 intersection
𝐵 is 0.2. And the probability of 𝐵 is
0.4. We should be careful not to use the
value of 0.3 as that’s the probability of 𝐴. Multiplying both the numerator and
denominator by five would give us the fraction of one-half. And that’s our answer for the first
part of the question.
The second question sounds
similar. But this time we’re working out the
probability of 𝐵 given 𝐴, so the formula will change slightly. On the numerator, we’ll still have
the probability of 𝐴 intersection 𝐵, but on the denominator, we’ll be using the
probability of 𝐴. Plugging in the values for each of
these probabilities, we have the fraction 0.2 over 0.3. Multiplying the numerator and
denominators by 10 gives us the fraction two-thirds. And that’s the answer for the
second part of the question.
