a die is rolled 10 times. find the chance of....
a)not getting 10 sixes
b)all the rolls showing 5 spots or less
I'm not sure how to do either, but for b, I think is it (5/6)^10 because each time there is a chance that the number will be 5 or less?
Please help. thank you!
a. Chance of getting 10 sixes = 1/6^10, then getting not sixes = 1 - 1/6^10
b. Same as a, since 5 or less would all be not 6s.
To find the probability of not getting 10 sixes when rolling a die 10 times, we need to consider the probability of getting any other outcome for each roll.
a) To calculate this probability, we can find the probability of getting a not six on one roll and raise it to the power of 10 since there are 10 rolls.
The probability of getting a not six on one roll is 1 - (1/6) = 5/6
So, the probability of not getting 10 sixes is (5/6)^10 ≈ 0.1615, or approximately 16.15%.
b) To find the probability of all rolls showing 5 spots or less, you are correct. The probability on each roll is 5/6 because there are 5 outcomes (1, 2, 3, 4, and 5) out of the 6 possible outcomes. So, the probability of all 10 rolls showing 5 spots or less is (5/6)^10 ≈ 0.1615, or approximately 16.15%.
To find the chance of not getting 10 sixes when rolling a die 10 times, you need to consider the probability of getting a six on each roll and calculate the complement of this probability.
a) The probability of getting a six on a single roll of a fair six-sided die is 1/6. Since the rolls are independent of each other, the probability of not getting a six on a single roll is 1 - 1/6 = 5/6.
To find the chance of not getting 10 sixes in 10 rolls, you need to multiply the probability of not getting a six on each roll. Since the rolls are independent, you can calculate this probability by raising the probability of not getting a six on a single roll (5/6) to the power of the number of rolls (10).
So the probability of not getting 10 sixes is (5/6)^10 ≈ 0.1615 or 16.15%.
b) For all the rolls to show 5 spots or less, your thinking is correct. On each roll, there are 5 outcomes (1, 2, 3, 4, or 5) out of 6 possibilities.
Since the rolls are independent, you can find the chance by multiplying the probability of getting 5 spots or less on each roll. So the probability is (5/6)^10 ≈ 0.1615 or 16.15%, which is the same as in part a).
Therefore, both parts a) and b) have the same probability of approximately 0.1615 or 16.15%.