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A study shows that the probability of a baby being born with gene x is 0.6. The probability of a baby being born with gene y is 0.7.

(a)What is the probability of being born with both genes assuming that the probabilities are independent?

(b)In fact; 90% of those born with gene x also have gene y. Of those born with gene y; what proportion also have gene x?
(c)Comment on the relative sizes of the confidence intervals for P(x) and P(y).
(d)If p(x) comes from a sample of 140 and p(y) from a sample of 210 are the true population proportions statistically different? State your hypotheses clearly and show all workings.
(e)Assuming p(x) is known to be true, what sample size would be required to make P(y) distinguishable from P(x) at 95% confidence? Show your workings.

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