You order sixteen burritos to go from a Mexican restaurant seven with hot peppers and none without. However the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. ( round your answer to the three decimal places. )
0.42
To find the probability of the given event, we need to determine the number of favorable outcomes (i.e., the number of ways we can pick three burritos with hot peppers) and the total number of possible outcomes.
Number of favorable outcomes:
Out of the 16 burritos, 7 have hot peppers. We need to pick three burritos with hot peppers. This can be calculated using the combination formula: C(n,r) = n! / (r!(n-r)!), where n is the total number of burritos with hot peppers (7) and r is the number of burritos we want to pick (3).
C(7, 3) = 7! / (3!(7-3)!) = (7! / (3! * 4!)) = (7 * 6 * 5) / (3 * 2 * 1) = 35
Therefore, there are 35 ways to pick three burritos with hot peppers out of the 16 burritos.
Total number of possible outcomes:
Since we are picking three burritos from a total of 16, this can be calculated using the combination formula as well:
C(16, 3) = 16! / (3!(16-3)!) = (16! / (3! * 13!)) = (16 * 15 * 14) / (3 * 2 * 1) = 560
Therefore, there are 560 ways to pick any three burritos out of the 16 burritos.
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 35 / 560
Rounding to three decimal places, the probability is approximately 0.062.