Question

A sample of 32 people yielded the information about their health insurance in the given table.Two people who provided information for the table were selected at random, without replacement. Find the probability that at least one has traditional insurance.The probability is(Type a fraction. Simplify your answer.)

Answer 1

From the table given

17 people have managed care plan

9 have Traditional insurance

6 have no insurance

The probability of an event happening is given as the ratio of the number of the possible outcome divided by the total outcome.

If two balls are taken, the probability that at least one has traditional insurance

TN or TM or TT or NT or MT

where T is for traditional insurance

N is for no insurance

M is for managed insurance

the probability that at least one of two people picked without replacement has traditional insurance

= 9/32 * 6/31 + 9/32 * 17/31 + 9/32 * 8/31 + 6/32 * 9/31 + 17/32 * 9/31

= (54 + 153 + 72 + 54 + 153)/992

= 486/992

= 243/496