6. For any married couple who are members of a tennis club, the probability that the husband has a degree is \(\frac { 3 } { 5 }\) and the probability that the wife has a degree is \(\frac { 1 } { 2 }\). The probability that the husband has a degree, given that the wife has a degree, is \(\frac { 11 } { 12 }\).
A married couple is chosen at random.
- Show that the probability that both of them have degrees is \(\frac { 11 } { 24 }\).
- Draw a Venn diagram to represent these data.
Find the probability that
- only one of them has a degree,
- neither of them has a degree.
Two married couples are chosen at random.
- Find the probability that only one of the two husbands and only one of the two wives have degrees.