In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win one prize.
A bag contains 3 red balls bearing numbers 1, 2, 3 (one number on one ball) ; and two black balls bearing numbers 4 and 6. A ball is drawn, its number noted and the ball is replaced in the bag. Then another ball is drawn and its number noted. Find the probability of drawing:
(i) 2 on the first draw and 6 on the second draw.
(ii) a number ≤ 2 on the first draw and 4 on the second draw.
(iii) a total of 5.
The balls are drawn with replacement.
∴ The sample space,
S = n(S) = 25
(i) Event A: 2 is drawn in the first draw and 6 in the second draw. A = {(2,6)}
n(A) = 1
∴ P(2 on the first and 6 on the second) = P(A) =
(ii) Event B : a number 2 in the first draw and 4 in the second draw.
B = {(1,4), (2,4)}
n(B) = 2
∴ P(number 2 in the first and 4 in the second draw) = P(B) =
(iii) Event C: a total of 5 is obtained C = {(1,4), (2,3), (3,2), (4,1)}
n(C) = 4
∴ P(a total of 5) = P(C) =