Question

1. In school lottery to win a price for "Free Domino's Pizza" it is required to select 5 numbers (in any order) out of 40 numbers.

What is the probability of winning?


2. Your sock drawer has 18 folded pairs of socks, with 8 pairs of white, 6 pairs of black, and 4 pairs of blue.

What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?

Answer 1

1/8 ;

12 / 51

Explanation:

To select any 5 numbers out of 40

Number of selection required / total numbers

Probability of winning = 5 /40 = 1/8

Total number of socks = 18

White, W = 8

Black, B = 6

Blue, C = 4

probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?

P(B) * [(P(C) + P(W)]

Probability = required outcome / Total possible outcomes

P(B) = 6 / 18 = 1/3

Without replacement :

P(W or C) = 8/17 + 4/17 = 12/17

Hence,

1/3 * 12/17

= 12 / 51