Thread: N is divided into 6 groups...find the probability

5. An auto insurance company has 10,000 policyholders. Each policyholder is classified as

(i) young or old;

(ii) male or female; and

(iii) married or single.

Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The
policyholders can also be classified as 1320 young males, 3010 married males, and 1400
young married persons. Finally, 600 of the policyholders are young married males.

How many of the company’s policyholders are young, female, and single?

The way I thought about this problem is:

X = 1 if young
X = 0 if old

Y = 1 if male
Y = 0 if female

Z = 1 if married
Z = 0 if single


So using the given numbers:

P(X) = 3000/10000 and P(X') = 7000/10000
P(Y) = 4600/10000 and P(Y') = 5400/10000
P(Z) = 7000/10000 and P(Z') = 3000/10000

P(XY) = P(Young Male) = 1320/10000
P(YZ) = P(Married Male) = 3010/10000
P(XZ) = P(Young Married) = 1400/10000
P(XYZ) = P(Young Male Married) = 600/10000

To get P(Young Female Single), use the law of total probability until you get all of the probabilities you need to calculate P(XY'Z'). For example:

P(XY) = P(XYZ) + P(XYZ')
P(XYZ') = P(XY) - P(XYZ) = 700/10000 = P(Young Male Single)

Etc.

thanks i got u......