The purpose of this problem is to help you judge which proba

The purpose of this problem is to help you judge which probability tools to use in a fairly complex problem. Consider a cross between two strains of peas that differ at all seven of the traits that Mendel used (a heptahydrate cross again). What proportion of the F2 offspring would you expect to show the dominant phenotype at any 5 of the 7 traits (and the recessive at the others)?

Solution

Let us suppose a cross between seven different traits as below:

AaBbCcDdEeFfGg × AaBbCcDdEeFfGg

Probability of getting any 5 of 7 dominant traits =

Probability of getting A from A and \'a\' is 1/2

Similarly, probability of getting B from B and \'b\' is 1/2

Probability of getting C from C and \'c\' is 1/2

Probability of getting D from D and \'d\' is 1/2

Probability of getting E from E and \'e\' is 1/2

Probability of getting f is 1/2

Probability of getting g is 1/2

Now probability of getting the above 5 dominant of 7 traits is 1/2 × 1/2 ×1/2×1/2×1/2×1/2×1/2= 1/128.

But it is given, any 5 of 7. Therefore there are many ways. No. Of ways = ⁵C₇ = 7!/5!(7-5)! = 21.

Therefore probability of getting any 5 out of seven traits = 21×1/128= 0.16