An insurance agent sells life, health and auto insurance. During the year she me

Question

An insurance agent sells life, health and auto insurance. During the year she met with 88 potential clients of these, 42 purchased life insurance, 40 health insurance, 24 auto insurance, 14 both life and health, 9 both life and auto, 11 both health and auto, and 2 purchased all A client is selected at random. Calculate the following probabilities (i) Client purchased no policies (ii) Client purchased only a health insurance policy (iii) Client purchased exactly one type of insurance (iv) Client purchased life or health but not auto insurance.

Explanation / Answer

here probabilty that client purcahsed at least one policy =42+40+24-14-9-11+2=74

hence (i) probability that client purcahsed no policy =85-74=11

(ii) purchased only a health policy =40-14-11+2=17

(iii)purcahsed exactly one type =42+40+24-2*(14+9+11)+3*2=44

(iv) purcahse life or health but not auto insurance =74-(auto insureance policy) =74-24=50

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