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anonymous

  • one year ago

13 peas are generated from parents having the green and yellow pair of genes, so there is 0.75 probability that an individual will have a green pod. Find the probability that the 13 offspring peas, at least 12 have green pods. Is it unusual to get 12 peas with green pods when 13 offsprings are generated

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  1. anonymous
    • one year ago
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    @oldrin.bataku

  2. anonymous
    • one year ago
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    how many ways can 12 of the 13 peas be selected (i.e. be green)?

  3. anonymous
    • one year ago
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    \(\binom{13}{12}=\binom{13}1=13\) such ways. now compute the probability of any particular such way: 12 peas green is \(0.75^{12}\) while the one pea not-green is \((1-0.75)^1=0.25\) so our total probability is: $$13\cdot0.75^{12}\cdot0.25\approx 0.1029$$

  4. anonymous
    • one year ago
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    so there's a ~10.3% chance this occurs randomly -- it's not super common, but not particularly unusual

  5. anonymous
    • one year ago
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    oops, you said at *least* 12 pods, so there is also the chance all thirteen are green

  6. kropot72
    • one year ago
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    To get the answer to the question it is necessary to add the probability that all 13 will be green. Therefore we need to find: \[\large (at\ least\ 12\ green)=0.1029+(0.75)^{13}=you\ can\ calculate\]

  7. anonymous
    • one year ago
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    in which case there's \(\binom{13}{13}=1\) such possible ways they can all turn green and the probability is \(0.75^{13}\approx 0.0238\) so our total probability is \(\text{probability 12 are green}+\text{probability all are green}\approx0.1029+0.0238=0.1267\)

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