5. Some state lotteries have a pick 3 game, where you can choose any number from...

5. Some state lotteries have a pick 3 game, where you can choose any number from 000 to 999. The state picks the winning number at random.

a) How many possible numbers can you choose from?

b) If all 3-digit numbers is equally likely what is the probability of any 1 specific number exactly matches the winning number?

c) Suppose you pick number 156 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

d) Suppose you pick the number 111 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

Solutions

Expert Solution

a) How many possible numbers can you choose from?

- The range is 000-999. Thus, there are total 1000 possible number to choose (Each digit can be selected in 10 ways and 3 such digits can be selected in 10^3 = 1000 ways)

b) If all 3-digit numbers is equally likely what is the probability of any 1 specific number exactly matches the winning number?

- If all 3-digit numbers are equally likely then, P(1 specific number exactly matches the winning number) = 1/1000 = 0.001

c) Suppose you pick number 156 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

- If order doesn't matter then these three digits can be arranged in 3! ways = 6 ways

And total events possible are 100

Thus, required probability = 6/1000 = 0.006

d) Suppose you pick the number 111 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

- Even though it is mentioned order doesn't matter, 111 can be selected only in 1 way

Thus. required probability = 1/1000 = 0.001

milcah answered 1 year ago

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