If events A and B are independent, then the probability of both A and B occurring is

P(A and B) = P(A) * P(B)

where P(A and B) is the probability of events A and B both occurring, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

a. a tail and a jack

P(tail) = 1/2

P(jack) = 4/52

P(a tail and a jack) = P(tail) * P(jack)

P(a tail and a jack) = (1/2)(4/52)

P(a tail and a jack) = 1/26

P(a tail and a jack) = 0.03846 or 3.846%

b. a head and a spade

P(head) = 1/2

P(spade) = 13/52 = 1/4

P(a head and a spade) = (1/2)*(1/4)

P(a head and a spade) = 1/8

P(a head and a spade) = 0.125 or 12.5%

c. a tail and a club

P(tail) = 1/2

P(club) = 13/52

P(club) = 1/4

P(a tail and a club) = (1/2)(1/4)

P(a tail and a club) = 1/8

P(a tail and a club) = 0.125 or 12.5%