Question

Brian's school locker has a three-digit combination lock that can be set using the numbers 5 to 9 (including 5 and 9), without repeating a number. The probability that the locker code begins with a prime number is %. The probability that the last digit of the locker code is an odd number is

Answer 1

Probability of a prime number = 2/5.

Probability of last number being odd = 3/5.

Explanation:

There are 2 prime numbers (5 and 7) in the 5 numbers ( 5, 6, 7, 8, 9).

So Prob(Prime number being first) = 2/5.

There are 3 odd numbers and 2 even so:

Possible combinations of Odd (O) and Even (E) numbers with last number being Odd are:

OOO, EEO, OEO or EOO.

Prob (OOO) = 3/5 * 1/2 * 1/3 = 3/30 = 1/10.

Prob(EEO) = 2/5 * 1/4 = 1/10.

Prob(OEO) = 3/5 * 1/2* 2/3 = 6/30 = 1/5.

Prob(EOO) = 2/5 * 3/4 * 2/3 = 12/60 = 1/5.

Therefore the probability of the last number being odd =

1/10 + 1/10 + 1/5 + 1/5

= 3/5 (answer).