What probability of offspring from cross PpYyRr x Ppyyrr is

What probability of offspring from cross (P_pY_yRr x P_pyyrr) is predicted to show the recessive phenotypes for at least two of the three characters?

Solution

From above given problem,

First use the information above to find all combinations that have at least two recessive phenotypes
First follow the black lines
PPYyRr, PPYyRr, PPYyrr, PPYyrr
Now follow the red lines
PPYyRr, PPYyRr, PPYyrr, PPYyrr
Continue this process until all of the combination are made with the other genotypes…Pp,Pp,pp
However, you will notice that Pp will give you the same as the other Pp so you do not have to go through those again….
Another note notice that you ignore the ones that don’t produce at least two recessive phenotypes…….
You should end up with
PPyyrr
Ppyyrr
ppyyRr
ppYyrr
ppyyrr

Now figure the probability that each one will occur

First determine the probability that each characteristic will show up…

PP ¼ Yy ½ Rr ½
Pp ½ Yy Rr
Pp yy ½ rr ½
pp ¼ yy rr

use this information to determine the probability of each individual……

PPyyrr ¼ x ½ x ½ = 1/16
Ppyyrr ½ x ½ x ½ = 1/8
ppyyRr ¼ x ½ x ½ = 1/16
ppYyrr ¼ x ½ x ½= 1/16
ppyyrr ¼ x ½ x ½ = 1/16

Now you have the individual probabilities for each of those offspring occuring…now add up those probabilities to get the probability that there will be at least two recessive phenotypes……

1/16 + 2/16 +1/16 + 1/16 + 1/16 = 6/16 = 3/8