Question

You order eighteen burritos to go from a Mexican restaurant, eight with hot peppers and ten without. However, the restaurant forgot to label them. If you pick five burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

All have hot peppers.

Answer 1

0.007

Explanation:

There are

• 8 burritos with hot peppers;
• 10 burritos without hot peppers.

Number of favorable outcomes (all 5 burritos are with hot peppers)

`=C^8_5=(8!)/(5!(8-5)!)=(8!)/(5!\cdot 3!)=(6\cdot 7\cdot 8)/(2\cdot 3)=56`

Number of all possible outcomes

`=C^(18)_5=(18!)/(5!(18-5)!)=(18!)/(5!\cdot 13!)=(14\cdot 15\cdot 16\cdot 17\cdot 18)/(1\cdot 2\cdot 3\cdot 4\cdot 5)=8,568`

The probability htat all 5 burritos are with hot peppers is

`(56)/(8,568)\approx 0.007`