4. The probability that an adult male is shorter than 66 inches is 0.3; that he is between 66 and 70 inches is 0.5; and that he is taller than 70 inches is 0.2. If two males are picked at random, find the probability that:
a. the heights of both are between 66 and 70 inches.
P(both between 66 and 70 in) = P(first between) * P(second between) = 0.5 * 0.5 = 0.25
b. the first is shorter than 66 inches and the second is taller than 70 inches.
P(first shorter and second taller) = P(first shorter) * P(second taller) = 0.3 * 0.2 = 0.06
c. the first is 70 inches or shorter and the second is 66 inches or taller.
P(first not taller than 70 and second not shorter than 66) = (1- P(first taller)) (1- P(second shorter)) = 0.8*0.7 = 0.56
In all parts we've used that P(A and B) = P(A) * P(B) for A,B independent events and P(not A) = 1 - P(A) for the calculation in part (c). I did not explain fully all the steps taken here, so please let me know if you would like any further explanations. I will be glad to help. Thank you!
Robert B.
07/30/25