Question

In a​ lottery, the top cash prize was ​$642 ​million, going to three lucky winners. Players pick five different numbers from 1 to 53 and one number from 1 to 46. A player wins a minimum award of $400 by correctly matching two numbers drawn from the white balls​ (1 through 53​) and matching the number on the gold ball​ (1 through 46​). What is the probability of winning the minimum​ award?

Answer 1

Answer:

$\frac{10}{53 \times 46 \times 26}$

Step-by-step explanation:

The probability of matching the number drawn on the gold ball is

$\frac{1}{46}$

The number of possible pairs of numbers from 1 to 53 is

$\binom{53}{2} = \frac{53 \times 52}{2} = 53 \times 26$

Choosing 5 numbers, you are choosing 10 different pairs:

$\binom{5}{2} = \frac{5 \times 4}{2} = 10$

Therefore the probability of correctly matching the drawn pair is

$\frac{10}{53 \times 26}$

Thus, the probability of winning (matching the pair AND the gold ball) is

$\frac{10}{53 \times 46 \times 26}$