Most tested B3.4

Chromosomal Sex Determination

This topic covers how sex is determined in mammals by the X and Y sex chromosomes. It focuses on using genetic diagrams, such as Punnett squares, to predict the probability and expected ratios of male and female offspring.

Part of the ESAT Biology syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.

Key points

  • In humans and most other mammals, biological sex is determined by a pair of sex chromosomes.
  • Females possess two X chromosomes (XX). All their egg cells (gametes) contain a single X chromosome.
  • Males possess one X and one Y chromosome (XY). They produce two types of sperm in equal proportions: half with an X chromosome and half with a Y chromosome.
  • The sex of the offspring is determined by the sperm cell that fertilizes the egg. If an X-carrying sperm fertilizes the egg, the offspring is female (XX). If a Y-carrying sperm fertilizes it, the offspring is male (XY).
  • Because there is an equal chance of either an X or a Y sperm fertilizing the egg, the theoretical probability of having a boy or a girl is 1/2 for each birth.
  • The expected ratio of male to female offspring in a large population is 1:1.

Formulae

P(Male Offspring) = 1/2

To find the probability of a single birth resulting in a male (XY).

P(Female Offspring) = 1/2

To find the probability of a single birth resulting in a female (XX).

P(Event A AND Event B) = P(A) × P(B)

To calculate the probability of a sequence of independent events, such as having a girl followed by a boy. Each birth is an independent event.

Definitions

Sex Chromosomes
The pair of chromosomes that determine an individual's biological sex. In humans, these are the X and Y chromosomes.
Gamete
A mature haploid reproductive cell (e.g., sperm or egg) which can unite with another from the opposite sex to form a zygote.
Punnett Square
A grid diagram used to predict the outcomes of a genetic cross by showing all possible combinations of parental gametes.

Worked example

A genetic cross is performed. Analysis of the offspring reveals 62 males and 58 females. A second cross using the same parent organisms results in four offspring. What is the probability that at least one of the four offspring is male?

  1. 1

    First, recognise that the initial data (62 males, 58 females) confirms the expected ~1:1 ratio.

    The probability of having a male (M) or female (F) in any single birth is 1/2.

  2. 2

    The question asks for the probability of 'at least one male'.

    It is simpler to calculate the probability of the opposite event ('no males') and subtract this from 1.

  3. 3

    The event 'no males' is the same as 'all four offspring are female'.

  4. 4

    The probability of one offspring being female is 1/2.

  5. 5

    Since each birth is an independent event, the probability of all four being female is P(F) × P(F) × P(F) × P(F) = (1/2)4.

  6. 6

    Calculate (1/2)4 = 1/16.

  7. 7

    The probability of 'at least one male' is 1 - P(all females) = 1 - 1/16.

  8. 8

    Calculate the final answer:

    1 - 1/16 = 15/16

Answer: 15/16

Common mistakes

  • ×Mistaking probability for certainty. A 1/2 probability does not guarantee that a couple with two children will have one boy and one girl.
  • ×Forgetting that each birth is an independent event. The sex of previous children has no influence on the sex of the next child.
  • ×Making arithmetic errors with fractions. For example, calculating (1/2)3 as 1/6 instead of 1/8. This is a common error under time pressure.
  • ×Confusing ratios with fractions. A 1:1 ratio of males to females means the fraction of males is 1/2, not 1.

No-calculator tips

  • ✓To find the total number of possible sex combinations for 'n' children, calculate 2n. For 3 children, there are 23 = 8 possible outcomes (BBB, BBG, etc.).
  • ✓When a question asks for 'at least one' of an outcome, it's almost always faster to calculate the probability of 'none' of that outcome and subtract from 1.
  • ✓Ratios in genetics questions can often be simplified. If you see 48 male offspring and 52 female offspring, immediately simplify this to approximately 1:1 for your calculations.

Read this topic in the official UAT-UK ESAT guide →

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