Question 1
2 marksTay-Sachs disease is caused by a recessive allele of a gene on an autosome. A couple who are both heterozygous for this gene plan to have three children.
Calculate the probability that at least one of their three children will have Tay-Sachs disease. Give your answer as a decimal to 2 significant figures.
Model answer
Probability that one child is unaffected = 3/4
Probability that all three are unaffected = (3/4)³ = 27/64 = 0.4219
Probability that at least one is affected = 1 - 27/64 = 37/64 = 0.578 = 0.58 (2 s.f.)
Explanation
Each child has a probability of 1/4 of being homozygous recessive, whatever happens to the others, because fertilisation is random. 'At least one' is easiest to work out as 1 minus the probability that none of the children is affected. Adding 1/4 three times is wrong: it counts some outcomes more than once and would exceed 1 for five children.
Mark scheme
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1 mark
Correct method, e.g. 1 - (3/4)³ or 1 - 27/64; or a correct final answer of 0.58 with no working
A correct answer of 0.58 with no working scores 2 marks. Accept for 1 mark: 0.42 or 27/64 (the probability that no child is affected) OR 37/64 or 0.578 (correct but not given as a decimal to 2 significant figures). Do not award this mark for 0.75 (1/4 added three times) or 0.016 (1/4 cubed: all three affected).
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1 mark
0.58
Do not accept 0.578, 0.6 or 58% for this mark.