In a hamster breeder's experience the number X of live pups in a litter has the probability distribution of x 3 4 5 6 7 8 9 P(x) 0.04 0.1 0.26 0.31 0.22 0.05 0.02 (a) Find the probability that the next litter will produce five to seven live pups. (b) Find the probability that the next litter will produce at least six live pups.

Let us write the above probabilities as shown below to aid our calculations.

$p(3)=p(x=3)=0.04$  

$p(4)=p(x=4)=0.1$

$p(5)=p(x=5)=0.26$

$p(6)=p(x=6)=0.31$

$p(7)=p(x=7)=0.22$

$p(8)=p(x=8)=0.05$

$p(9)=p(x=9)=0.02$

a.

The probability that the next litter will produce five to seven live pups is given as,

$p(5)+p(6)+p(7)=0.26+0.31+0.22=0.79$

Thus, the probability that the next litter will produce five to seven live seven pups is 0.79.

b.

The probability that the next litter will produce at least six live pups is given as,

$p(6)+p(7)+p(8)+p(9)=0.31+0.22+0.05+0.02=0.60$

Therefore, the probability that the next litter will produce at least six live pups is 0.60.