The probability of winning something on a single play at a slot machine is 0.29. After 6 plays on the slot machine, What is the probability of winning at least once?
Write only a number as your answer. Round your answer to four decimal places (for example: 0.7319). Do not write as a percentage.
The best strategy to solve it to find the probably of loosing every tie and subtracting that from all the possible combinations.
0.8867
To find the probability of winning at least once in 6 plays on the slot machine, we can use the complement rule.
The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
The probability of not winning on a single play at the slot machine is 1 - 0.29 = 0.71.
Since each play is independent of the others, the probability of not winning in 6 plays is (0.71)^(6).
So, the probability of winning at least once in 6 plays is 1 - (0.71)^(6).
Calculating this, we find:
1 - (0.71)^(6) ≈ 0.8681
Therefore, the probability of winning at least once in 6 plays at the slot machine is approximately 0.8681.
To find the probability of winning at least once in 6 plays, we can find the probability of losing all 6 times and subtract it from 1.
The probability of losing on a single play is the complement of winning, which is 1 - 0.29 = 0.71.
Since each play is independent, the probability of losing all 6 times is simply the product of the individual probabilities of losing:
P(losing all 6 times) = (0.71)^6
To find the probability of winning at least once, we subtract this value from 1:
P(winning at least once) = 1 - P(losing all 6 times) = 1 - (0.71)^6
Calculating this value, we get:
P(winning at least once) ≈ 1 - (0.71)^6 ≈ 0.9497
Rounding this to four decimal places, the probability of winning at least once after 6 plays on the slot machine is approximately 0.9497.
Therefore, the answer is 0.9497.