Ana is choosing a pillow for her bed. The probability that the pillow is encased in microfiber is 0.5 . The probability that the pillow is filled with memory foam is 0.7. The probability that the pillow is filled with memory foam and encased in microfiber is 0.3. Which equation shows the correct use of the addition rule to determine the probability that the pillow is either encased in microfiber or filled with memory foam?

P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 0.7 - 0.3 = 0.9

Step-by-step explanation:

The equation we should use to calculate the addition of probabilities is:

P(A or B) = P(A) + P(B) - P(A and B)

Notice that if we just sum P(A) + P(B), our result would be wrong, because we would sum the intersection of those events two times.

So, in this case, if we call 'A' the pillow being encased in microfiber and 'B' the pillow being filled with memory foam, we have that:

P(A) = 0.5

P(B) = 0.7

P(A and B) = 0.3

So the addition of both probabilities is:

P(A or B) = 0.5 + 0.7 - 0.3 = 0.9