Question 1081354: A fair die is rolled 4 times. What is the probability that a 2 is obtained on at least one of the rolls? Round your answer to three decimal places .
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! For a single die, the probability of rolling a "2" is 1/6 since there's only one way to get a "2" out of 6 possible outcomes (1 through 6).
For a single die, the probability of not rolling a 2 is 5/6 because there are 5 ways to get a non "2" result (1,3,4,5,6).
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Assuming each roll is independent, and you roll the die four times, this would mean the probability of not rolling a 2 at all would be (5/6)*(5/6)*(5/6)*(5/6) = 0.48225308641976
This is approximate. Subtract that result from 1 to get
1-0.48225308641976 = 0.51774691358023
which is also approximate
Rounding to three decimal places gives: 0.518
Final Answer: 0.518
Note: 0.518 = 51.8%
Another note: the events "rolling 4 times and not getting a two at all" and "rolling 4 times and getting at least one two" are complementary events. One or the other must happen. The sum of their respective probabilities is equal to 1.
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