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
