Question

11.9.27 Assigned Media Question Help A car rental agency has 14 midsized and 16 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability that the cars selected consist of all midsized cars. What is the probability that the cars selected consist of all midsized cars? (Type an integer or decimal rounded to four decimal places as needed.) P Enter your answer in the answer box and then Click Check Answer. All parts showing Clear All Check Answer all 5:57 PM Next Sunday 11/10/201 Previous

Answer 1

Solution:

Given:

14 midsized cars
16 compact cars
total 30 cars
we have to select 6 cars.
Find:
P( All midsized cars) =..........?

6 midsized cars can be selected from 14 midsized cars in ₁₄C₆ ways.

6 any cars can be selected from 30 any cars in ₃₀C₆ ways.

Thus

P(All Midsized Cars) = 1406 30C6

Use following combination formula:

n! nort! x (n-1)!

14! (14 - 6)! 14! 6 x 8! 14 x 13 x 12 x 11 x 10 x 9 x 8! 6 x 5 x 4 x 3 x 2 x1 x 8! 1466!

14C6 = 14 x 13 x 12 x 11 x 10 x 9 6 x 5 x 4 x 3 x 2 x 1

14C6 = 3003

and

30! ! X (30 - 6)! 30! 301 6 x 24! 30 x 29 x 28 x 27 x 26 x 25 x 24! 6 x 5 x 4 x 3 x 2 x 1 x 24! 3006 6

30 x 29 x 28 x 27 x 26 x 25 30 C6 = - 6 x 5 x 4 x 3 x 2 x1

30 C6 = 593775

Thus

P(All Midsized Cars) = 1406 30C6

3003 P(All Midsized Cars) = =

P(All Midsized Cars) = 0.0050575

P(All Midsized Cars) = 0.0051