Question

Two tickets are drawn from a box with 5 tickets numbered as follows: 1,1,3,3,5. If the tickets are drawn with replacement, find the probability that the first ticket is a 1 and the second ticket is a 5. If the tickets are drawn without replacement, find the probability that the first ticket is a 1 and the second ticket is a 3. If the tickets are drawn without replacement, find the probability that the first ticket is a 1 and the second ticket is a 1

Answer 1

(a) With replacement

P (first ticket is 1 and second ticket is 5)

P(first ticket =1) =2/5

P(second ticket = 5) = 1/5

P (first ticket is 1 and second ticket is 5) = 2/5 * 1/5 = 2/25 = 0.08

(b) without replacemnet

P (first ticket is 1 and second ticket is 3)

P (first ticket is 1) = 2/5

P(second ticket is 3) = 2/4 [as one ticket is already removed]

P (first ticket is 1 and second ticket is 3) = 2/5 * 2/4 = 4/20 = 0.20

(c) withour replacement

P(first ticket is 1 and second is 1)

P(first ticket is 1) = 2/5

P(second ticket is 1)= 1/4

P(first ticket is 1 and second is 1) = 2/5 * 1/4 = 2/20 = 0.10