Question

In a lottery, the top cash prize was $693 million, going to three lucky winners. Players pick five different numbers from 1 to 51

and one number from 1 to 42. -
A player wins a minimum award of $400 by correctly matching four numbers drawn from the white balls (1 through 51) and
matching the number on the gold ball (1 through 42). What is the probability of winning the minimum award?
The probability of winning the minimum award is.
(Type an integer or a simplified fraction.)

Answer 1

1/237.12.

Explanation:

The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.

The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:

(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)

= (51 choose 4) / (51 choose 5)

= 51! / (4! * 47!) / (51! / (5! * 46!))

= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)

= 19600 / 10,946

= 1/5.6 approximately

The probability of picking 1 number correctly from 1 to 42 is given by the formula:

1/42

The final probability of winning the minimum award is given by multiplying the above two probabilities:

1/5.6 * 1/42 = 1/237.12

So, the probability of winning the minimum award is approximately 1/237.12.