For a fair coin tossed three times, the eight possible simple events are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Let X = number of tails. Find the probability distribution for X by filling in the table showing each possible value of X along with the probability that value occurs. k=0,1,2,3 P(X=k)

Question

For a fair coin tossed three times, the eight possible simple events are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Let X = number of tails. Find the probability distribution for X by filling in the table showing each possible value of X along with the probability that value occurs. k=0,1,2,3  P(X=k)

Reiny · Accepted Answer

k _____ P(x=k)
0 ....... C(3,0)(1/2^0(1/2^3 = 1/8
1 ....... C(3,1)(1/2^1(1/2)^2 = 3/8
2 ....... C(3,2)(1/2)^2(1/2)^1 = 3/8
3 ........ C(3,3)(1/2)^3(1/2)^0 = 1/8

notice the sum of those is 1, as it should be.