Question

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 decimal places). (a) 0.225 (b) 0.275 (c) 0.325 (d) 0.375 (e) 0.425 IA on Ib NIN

Answer 1

(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.