You order sixteen burritos to go from a Mexican restaurant: seven with hot peppers and nine without. However, the restaurant forgot to label them. If you pick four burritos at random, find the probability that at least two of the burritos you pick have hot peppers.
i can figure out how see if they are all hot
7C4/16C4 which is 0.019.
but i cant get the probably of 2 being hot. i thought it was
9C2*7C2/16C4 but it keeps saying that it is wrong.
To find the probability that at least two of the burritos you pick have hot peppers, you can subtract the probability of picking 0 or 1 burrito with hot peppers from 1.
First, let's find the probability of picking 0 burritos with hot peppers:
Since there are 9 burritos without hot peppers and you are picking 4 burritos, the number of ways to pick 4 burritos without hot peppers is 9C4 (combinations).
The total number of ways to pick any 4 burritos out of the 16 burritos is 16C4.
So, the probability of picking 0 burritos with hot peppers is 9C4 / 16C4.
Next, let's find the probability of picking 1 burrito with hot peppers:
Since there are 7 burritos with hot peppers and you are picking 4 burritos, the number of ways to pick 1 burrito with hot peppers is 7C1, and the number of ways to pick the remaining 3 burritos without hot peppers is 9C3.
Again, the total number of ways to pick any 4 burritos out of the 16 burritos is 16C4.
So, the probability of picking 1 burrito with hot peppers is (7C1 * 9C3) / 16C4.
Finally, to find the probability of at least two burritos having hot peppers, you subtract the probability of picking 0 or 1 burrito with hot peppers from 1:
Probability = 1 - (9C4 / 16C4) - [(7C1 * 9C3) / 16C4].
By calculating this expression, you will find the desired probability.