Question 1

Screenshot taken from Coursera

Question 2

Screenshot taken from Coursera

Answer

P(k=2) = $\large\frac{3!}{2! \times 1!} \times 0.51^2 \times 0.49^1$ = $3 \times 0.2601 \times 0.49$ = 0.382

Question 3

Screenshot taken from Coursera

Question 4

Screenshot taken from Coursera

Answer

Question 5

Screenshot taken from Coursera

Question 6

Screenshot taken from Coursera

Answer

  • This is a problem of conditional probability

  • P(identical) = 0.3

    • P(both females | identical) = 0.5
    • P(both males | identical) = 0.5

=> P(both females and identical) = $0.3 \times 0.5$ = 0.15

  • P(fraternal) = 0.7
    • P(both females | fraternal) = 0.25
    • P(both males | fraternal) = 0.25
    • P(mixes| fraternal) = 0.5

=> P(both females and fraternal) = $0.7 \times 0.25$ = 0.175

Bayes' theorem

=> P(identical | both females) = $\large\frac{P(\text{both females and identical})}{P(\text{both females})}$ = $\large\frac{0.15}{0.15 + 0.175}$ = 0.4615

Question 7

Screenshot taken from Coursera