a)
P(Peter lands exactly 4 licks)=P(X=4)=^{8}C_{4}(0.7)^{4}*(0.3)^{4} =0.1361
b)
P(at least 2 licks)=P(X>=2) =1-P(X<=1)=1-(P(X=0)+P(X=1))=1-( ^{8}C_{0}(0.7)^{0}*(0.3)^{8} +^{8}C_{1}(0.7)^{1}*(0.3)^{7} )
=0.9987
hence P(Peter lands exactly 4 licks given at least 2 licks)=P(X=4|X>=2)=0.1361/0.9987=0.1363
Question 3: My dog Peter lies to lick Jack, his cat companion. Because Jack prefers not...