One of my kids frequently tries to get his way by asking for permission for a tr

Question

One of my kids frequently tries to get his way by asking for permission for a treat from “Mom” or “Dad.” Let M be the event that the Mom said yes and D be the event that the Dad says yes. Suppose that M and D are independent events with P(A)=.4 and P(B) = .7

a)What is the probability that both Mom and Dad will say no? Write out the probability in mathematical symbols as well as calculate probability
b)What is the probability that either Mom or Dad will say yes? Write out the probability in mathematical symbols as well as calculate probability.

Explanation / Answer

Given P(A) = 0.4, Therefore P(Ac) = 1-0.4 = 0.6 also P(B) = 0.7, Therefore P(Bc) = 1-0.7 = 0.3

(a) Probability that both mom and dad say no = P(Ac)*P(Bc) = 0.6 * 0.3 = 0.18

(b) Probability that either Mom or dad will say yes = P(Dad says yes, mom says no) + P(Dad says no, mom says yes) = P(A) * P(Bc) + P(Ac) * P(B) = (0.4 * 0.3) + (0.6 * 0.7) = 0.12 + 0.42 = 0.54

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