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Jim C
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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?

Jim C :

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


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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