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Grade 10 · lesson 3 of 4

Combine Independent Offspring Chances

Calculate a short sequence probability under explicit independence.

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Supplied materials

  • Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.

Learn the idea

For a fictional Pp × pp cross, white probability is 1/2 and purple probability is 1/2 per offspring. Assume independent allele contributions and independent offspring outcomes with unchanged parents and conditions. For two particular ordered outcomes, multiply their probabilities. The first result does not make the next result “due” to be a different color.

List the two-offspring color sequences: purple-purple, purple-white, white-purple, white-white. Under the independence assumption each has probability (1/2)(1/2) = 1/4. Exactly one white includes two sequences, so its probability is 1/4 + 1/4 = 1/2. At least one white excludes only purple-purple, giving 1 − 1/4 = 3/4. These are chances for a repeated model, not guarantees for a particular pair.

  1. Write the four ordered two-offspring sequences.
  2. Multiply 1/2 by 1/2 for each sequence.
  3. Add the two sequences with exactly one white.
  4. Use the complement to find at least one white.
Worked example

See the method in action

Both white: 1/4. Exactly one white: 1/2. At least one white: 3/4. These events differ, so label the event before calculating.

Your turn

Check your reasoning

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What is the probability that both of two independent offspring are white in this Pp × pp model?

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See the answer and explanation

1/4

Both requires white on the first and second outcomes, so (1/2)(1/2) = 1/4.

Take it further

Change to three independent offspring with the same 1/2 white chance. All three white has probability (1/2)³ = 1/8; at least one white is 1 − (1/2)³ = 7/8.

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