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Jim C, Teacher

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Experience: MST Math Education 1991 experience teaching high school and college

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A ram was bred to four known carriers of a recessive allele.

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A ram was bred to four known carriers of a recessive allele. Each of the ewes had normal twin lambs. How confident are we that the ram does not carry this recessive allele?

The twin lambs were normal but were they identical twins or fraternal twins.

Customer:

This is a homework question. That is all the information I was given.

Jim C :

The twin lambs were normal but were they identical twins or fraternal twins? Assuming fraternal twins that means 8 independent offspring all normal. If the ram were a carrier this result would happen only once every 2 to the 8th power times or 1/256 times.

At this point we need some additional information. What was the probasbility of the ram being a carrier before these tests? If it was originally 1:1 we could also say it was 256:256 carrier to normal. But only 1 time in 256 would the carrier possibliity give rise to the results we got, while we would get those results every time if the ram were not a carrier. So the odds would now be 1:256 carrier to non-carrier. That would mean 1/257 chances of being a carrier.

Jim C :

Note if the original probability of being a carrier were p with a probability of q of not being a carrier (with p+q=1 of course) the odds would be p to q or 256p to 256q before the test After the test the 256p would become just p while the 256q would stay 256q. We would get a ration of p to 256q after the test or a proability of being a carrier of p/(p+256q). This is likely to be close to (1/256)(p/q).

Jim C :

Example if the odds of being a carrier in general, for someone without the trait, were 1/1001 then the ratio of p to q would be 1/1000. After our test these would drop to very close of 1/256000. If you insist on being precise they would be 1/256001.

Jim C :

Depending on the number of identical twins our 2 to the 8th could be as low as 2 to the 4th and we would replace 256 with 16 for all identical twins, 32 for 3 pairs of idential twins 64 for two pair and 128 for 1 pair of identical twins.

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