QUESTION: Caitlin likes to finish her homework as early as she can. The probability that she has a math homework tonight is 0.63 and the probability that she has science homework tonight is 0.22. If the probability that Caitlin had both math and science homework tonight is 0.13 then what is the probability that she has neither math homework nor science homework tonight?
GIVEN:
P(Math) = 0.63
P(Science) = 0.22
P(Math & Science) = 0.13
ASKED: P(Neither Math nor Science)
FORMULA: P(Neither Math nor Science) = 1 - P(Math or Science)
SOLUTION:
In order to find what is asked, we needed to find first the P(Math or Science).
P(Math or Science) = P(Math) + P(Science) - P(Math and Science)
P(Math or Science) = 0.63 +0.22 -0.13
P(Math or Science) = 0.72
Next, we should substitute the value we got to the formula given above.
P(Neither Math nor Science) = 1 - P(Math or Science)
P(Neither Math nor Science) = 1 - 0.72
P(Neither Math nor Science) = 0.28
ANSWER: The probability that Caitlin has neither Math homework nor Science homework is 0.28. In the choices, it is the letter C.