Answer to Question #131766 in Statistics and Probability for Regomoditswe Moremedi

Question

The probability that a customer will buy a cup of coffee is 0.6. A customer buys a muffin 45% of the time when a cup of coffee is bought, but only 10% of the time when a cup of coffee is not bought.

1. What is the probability of buying a muffin but not a cup of coffee.

2. What is the probability of buying a muffin

Answer 1

Let:

Buying coffee = C

Buying muffin = M

P(C) =0.6

P(M/C)=0.45

P(M/C')=0.1

Solution to Q.1

P(M and C') = P(C').P(M/C')

but P(C') = 1- P(C) = 0.4

Thus, P(M and C')=$0.4*0.1 = 0.04$

Answer: 0.04

Solution to Q.2



P(M) = P(C).P(M/C) + P(C').P(M/C')

$$=(0.6)(0.45) + (0.1)(0.4)$$ $$=0.31$$

Answer: 0.31