The seeds of the garden pea Pisum satiyum are either yellow

The seeds of the garden pea (Pisum satiyum) are either yellow or green. A certain cross between pea plants produces progeny in the ratio: 3 yellow for every 1 green. Given that four randomly chosen progeny of such a cross are examined, define Y as the number of yellow pea plants chosen.

Find the typical range of the number of yellow peas drawn from a random draw of 4 peas expressed as the 1st SD window.

Solution

Sounds that n=4

Since Y is yellow and 3 out of 4 is yellow then p=3/4=0.75 then q=1-p=1/4=0.25

a)P(Y=3) =4C3(0.75)^3(0.25)^1=0.4219


b)P(Y=4) =4C4(0.75)^4=0.3164


c)P(Y=4 union Y=0)=P(Y=4)+P(Y=0)

=0.3164+4C0(0.75)^0(0.25)^4

=0.3164+0.0039=0.3203