Question

In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 1 to 80. A total of 20 winning numbers are randomly selected and displayed on a screen. If you choose a single number, your probability of selecting a winning number is 2080, or 0.25. Suppose Lester plays the Quick Draw lottery 10 times. Each time, Lester only chooses a single number. What is the probability that he loses all 10 of his lottery games? Please give your answer to three decimal places.

Answer 1

0.056

Explanation:

Data provided in the question;

Probability of winning, p = 0.25

Probability of losing, q = 1 - Probability of winning

= 1 - p = 1 - 0.25

= 0.75

Number of times lottery is drawn, n = 10

Now,

P( he loses all 10 of his lottery games ) = qⁿ

on substituting the respective values, we get

P( he loses all 10 of his lottery games ) = 0.75¹⁰

or

P( he loses all 10 of his lottery games ) = 0.056