Five balls are numbered 1 to 5 Three balls are randomly pick

Five balls are numbered 1 to 5. Three balls are randomly picked from them.

a) Write down sample space.

b) Define A: ball 2 is picked. find p(A)

c) Define event B: Ball 1 is picked. Find P(B)

d) Compute the probability of picking ball 2 given ball 1 is picked.

a)The sample space is 5C3=10 combinations.

S={(1,2,3), (1,2,4), (1,2,5), (1,3,4),(1,3.5),(1,4,5),(2,3,4),(2,3,5),(2,4,5),(3,4,5)}

b)P(A)=6/10

c)P(B)=6/10

d)The probability of picking ball 2 given ball 1 is picked is: 3/10