Question

He must spend no more than $300 on it—he goes to Lowes and tells this condition to the salesperson (a big storm has blown all the price tags off the grills.) She smiles and says: “you’re in luck: out of our 16 grills, all but two of them meet that condition.” With an air of confidence about him, my brother-in-law charges into the sea of grills and picks two at random. a. How many ways can he do this and pick exactly one that costs no more than $300? b. How many ways can he do this and pick both costing more than $300? c. What is the probability that he hasn’t completely wasted his time, that is, at least one of them costs no more than $300?

Answer 1

ANSWER OF PART a:

Given,

Of the 16 grills, only two of them satisfy the condition," He must spend no more than $300 on it".

No. of ways of picking exactly one grill  out of 2= 2

If one grill is picked, then he has to pick another grill from the remaining 16-2=14 grills and that can be done in 14 different ways.

Hence, no. of ways of picking exactly one grill that costs no more than $300=214=28 ways.

ANSWER OF PART b:

Since, 14 grills cost more than $300

Therefore, Number of ways of picking both more than $300== 91 different ways.

ANSWER OF PART c:

No. of ways of picking 2 grills from 16 grills== 120

Probability,

P(at least one of them costs no more than $300)= 1- P(both of them costing greater than $300)

= 1- /= 1- 91/120

= 29/120