A tool box contains 12 bolts and 10 nuts. If a handyman grabs 8 items randomly, what is the probability that he gets four bolts and four nuts? (The answer is rounded to three de…

Question

asked Apr 20, 2020 20.0k views

1 Answer

Aakinlalu · Answer 1 · 2020-04-26T05:09:22+0000

Answer:

(c) 0.325

Explanation:

Given,

The number of bolts = 12,

Numbers of nuts = 10,

Total items = 12 + 10 = 22

Thus, the number of ways of choosing 8 items out of 22 items = C(22,8)

Now, the number of ways of choosing 4 bolts and 4 nuts = C(12, 4) × C(10, 4)

Hence, the probability of getting four bolts and four nuts

$=\frac{\text{ways of choosing 4 nuts and 4 bolts}}{\text{Total ways of choosing 8 items}}$

=(C(12,4)* C(10,4))/(C(22, 8))

=((12!)/(4!8!)* (10!)/(4!6!))/((22!)/(8!14!))

=(495* 210)/(319770)

=0.325077399381

$\approx 0.325$

Therefore, option (c) is correct.