Consider 2 trials each having the same probability of succes

Consider 2 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X]=0.4 and P{X=2}= 0 what are the possible values of P{X=0} and P{X=1}?

Solution

let P[X=0]=a   and P[X=1]=b and it is given that P[x=2]=0

X denotes the total number of successes in 2 trials

so X xan take the values 0,1,2

now total probability should be 1

so P[X=0]+P[X=1]+P[X=2]=1     or, a+b+0=1        or, a+b=1

given that E[X]=0.4

or, 0*P[X=0]+1*P[X=1]+2*P[X=2]=0.4

or, 0*a+1*b+2*0=0.4

or, b=0.4

hence a=1-b=1-0.4=0.6

so possible values of P[X=0] and P[X=1] are

P[X=0]=0.6 and P[X=1]=0.4 [answer]