Video Transcript
Suppose that 𝐴 and 𝐵 are two
events. Given that the probability of 𝐴
minus 𝐵 is equal to two-sevenths and the probability of 𝐴 intersection 𝐵 is
one-sixth, determine the probability of 𝐴.
We begin this question by recalling
the difference rule for probability. This states that the probability of
𝐴 minus 𝐵 is equal to the probability of 𝐴 minus the probability of 𝐴
intersection 𝐵. We are told that the probability of
𝐴 minus 𝐵 is equal to two-sevenths and the probability of 𝐴 intersection 𝐵 is
one-sixth. Substituting these values into our
formula, we have two-sevenths is equal to the probability of 𝐴 minus one-sixth. In order to calculate the
probability of 𝐴, we can add one-sixth to both sides of this equation. The probability of 𝐴 is equal to
two-sevenths plus one-sixth.
In order to add any two fractions,
we begin by finding a common denominator. In this case, we’ll use 42 as this
is the lowest common multiple of seven and six. Multiplying the numerator and
denominator of our first fraction by six gives us 12 over 42, and multiplying the
numerator and denominator of the second fraction by seven gives us seven over
42. Two-sevenths plus one-sixth is
therefore equal to 19 over 42. We can therefore conclude that the
probability of event 𝐴 is 19 over 42.
