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In a New York State daily lottery game, a sequence of four digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that three of the four digits are the same.

In a New York State daily lottery game, a sequence of four digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that three of the four digits are the same.

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago
Total possible ways = 10^4

Now, there are 4 different combinations where there are 3 digits that are the same (Ex: 0001, 0010, 0100, 1000). For each of those, there are 10 different possible digits that can be repeated 3 times in the sequence, and 10 digits that aren't necessarily repeated (9 if we limit the condition to only 3 of 4 and excluding 4 of 4).

So, that leaves us with a probability of 4*10*10/10^4 = 4/100 = 1/25 = .04

Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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