Question

The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .(a) What is the probability that the winning number matches your number exactly?(Enter your answer rounded to four decimal places.)=(b) What is the probability that the winning number has the same digits as your number in any order?(Enter your answer rounded to four decimal places.)

Answer 1

Explanation:

Given that the Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .

a) The probability that the winning number matches your number exactly

= 1 out of 10000 = 0.0001

b) the probability that the winning number has the same digits as your number in any order

This includes 0379, 0397, 0739, 0793, 0937, 0397 i.e. starting from 0 there are 6 = 3! ways

Or 3079 can be arranged in 4! ways = 24

Favorable outcomes = 24

Prob of winning = 24/10000 = 0.00024

=0.0002