Question

1. In the Texas Pick-3, three numbers are drawn (with repetition) from 0 through 9 and order does matter (so picking 426 is different than 246). You win $500 if you get the right three numbers in the right order. (a.) How many possible tickets are there? What is the probability you win $500? (b.) You can also win $80 if you obtain the right three numbers in any other order. What is the probability you win this prize? (c.) What is the probability that the three numbers drawn are distinct?

Answer 1

There are 10 single digit numbers from 0 - 9

(a) Total Possible tickets (with repetition) = 10 * 10 * 10 = 1000

Probability = Favorable Outcomes / Total Outcomes

Probability of winning = 1 (only 1 number in the correct order

Therefore the required probability = 1 / 1000 = 0.001

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(b) Probability = Favorable Outcomes / Total Outcomes

Favorable outcomes

If 3 distinct numbers are picked: Then number of outcomes = 3! = 6

If 2 similar and 1 distinct number is picked: Then number of outcomes = 3

If 3 similar numbers are picked: Then number of outcomes = 1

Therefore Total Favorable outcomes = 10

The Required probability = 10 / 1000 = 1 / 100 = 0.01

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(c) Probability that the 3 numbers are distinct

Favorable outcomes = 10 * 9 * 8 = 720

Therefore the required probability = 720 / 1000 = 72 / 100 = 18 / 25 = 0.72

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