Question 1
2 marksHuman body cells contain 23 pairs of homologous chromosomes. One chromosome of each pair came from the person's mother and the other from the person's father.
Ignoring crossing over, calculate the probability that a gamete produced by a person contains only chromosomes that came from that person's mother.
Give your answer in standard form to 2 significant figures.
Model answer
For each of the 23 pairs, the probability that the gamete receives the chromosome from the mother is 1/2, and the pairs segregate independently.
Probability = (1/2)²³ = 1 ÷ 8 388 608 = 1.19 × 10⁻⁷ = 1.2 × 10⁻⁷
Explanation
Because each homologous pair lines up independently in meiosis I, the chance of the maternal chromosome going into a gamete is 1/2 for each pair, and independent probabilities are multiplied. This is the same idea as the 2ⁿ combinations: the all-maternal gamete is just one of 2²³ equally likely combinations. A common error is to use 46 chromosomes instead of 23 pairs.
Mark scheme
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1 mark
Correct method, e.g. (1/2)²³ or 1 ÷ 2²³ (= 1 ÷ 8 388 608); or a correct final answer of 1.2 × 10⁻⁷ with no working
A correct answer of 1.2 × 10⁻⁷ with no working scores 2 marks. Accept for 1 mark: 1.19 × 10⁻⁷ or 1.192 × 10⁻⁷ (not to 2 significant figures) OR 0.00000012 (not in standard form) OR 1/8 388 608. Reject 1/46, 1/23 and (1/2)⁴⁶ for any mark.
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1 mark
1.2 × 10⁻⁷