What is the probability of rolling at least one 6 with four rolls of a fair die?
A fair six sided die is thrown . Find the probability of getting a4
No Michael, that is not right
The key word is "at least one six", meaning it could be one six, two sixes, thre or four sixes.
What we don't want is NO sixes
So to calculate the prob of no sixes in 4 tries is (5/6)^4
So the prob of at least one six is
1 = (5/6)^4
= .5177
To determine the probability of rolling at least one 6 with four rolls of a fair die, we need to consider the possible outcomes and calculate the favorable outcomes.
First, let's calculate the probability of not rolling any 6 in one roll. Since there are six equally likely outcomes (numbers 1 to 6) on a fair die and only one outcome (6) corresponds to a successful roll, the probability of not rolling a 6 on one roll is 5/6.
Now, since each roll is an independent event, we can use the multiplication rule. Therefore, the probability of not rolling a 6 in four rolls is (5/6) * (5/6) * (5/6) * (5/6), which simplifies to (5/6)^4.
To find the probability of rolling at least one 6, we subtract the probability of not rolling any 6 from 1 (because the sum of all possible outcomes must equal 1). Therefore, the probability of rolling at least one 6 with four rolls of a fair die is 1 - (5/6)^4.
To calculate this probability, we need to raise 5/6 to the power of 4 and subtract the result from 1.
Each time you roll, your probability of rolling a 6 is 1/6.
You have four rolls, so multiply by 4 to get 4/6, or 2/3.