Statistics f.4(20marks!!!!!!!)

1. In a casino, a slot machine has 3 circular slots and each slot has 6 symbols on it, namely, bell, orange, cherry, lemon,star and bar.When the arm of the machine is pulled down, the slots rotate independently and then stop so that the outcome is a random combination of one symbol from each slot. what is the probability of getting 2 cherries?

1/6 x 1/6 x 5/6 + 1/6 x 5/6 x 1/6 + 5/6 x 1/6 x 1/6
= 1/6 x 1/6 x 5/6 x 3
= 5/72

2. A number lock has four rings, each with 10 different digits 0,1,2,...,9.
a) how many possible 4-digit numbers can be made?
10 x 10 x 10 x 10 = 10,000

b) If a number is selected at random, what is the probability that
(1) the number is a multiple of 5?
1/5 as last number is zero or 5 will be a multiple of 5 (2/10 = 1/5)
(2) the first two digits are even?
1/2 x 1/2 = 1/4
(3) the number is composed of digits 3 and 8 only?
2/10 x 2/10 x 2/10 x 2/10 = 1/625