Edexcel S1 Specimen — Question 6

Exam BoardEdexcel
ModuleS1 (Statistics 1)
SessionSpecimen
TopicConditional Probability
TypeGiven conditional, find joint or marginal

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.
  1. Show that the probability that both of them have degrees is \(\frac { 11 } { 24 }\).
  2. Draw a Venn diagram to represent these data. Find the probability that
  3. only one of them has a degree,
  4. neither of them has a degree. Two married couples are chosen at random.
  5. Find the probability that only one of the two husbands and only one of the two wives have degrees.