Question

PLEASE HELP! (STATS) A box contains 10 batteries of which 6 are still working. Jada starts picking batteries one at a time without replacement from the box and testing them to see if they work. Find the probability that all of the first 3 she chooses will work?

Group of answer choices

0.120

0.167

0.600

0.216

0.037

Answer 1

Answer: 0.167

Explanation:

Given: Total batteries = 10

Batteries that are still working = 6

Number of ways to pick 3 working batteries =
`^6C_3=(6!)/(3!3!)`

`=(6*5*4*3!)/(6*3!)\\\\=20`

Number of ways of pick 3 batteries out of 10 =

`^(10)C_3=(10!)/(3!7!)=(10*9*8*7!)/(6*7!)\\\\=120`

Required probability =
`(20)/(120)=0.167`

Hence, the probability that all of the first 3 she chooses will work = 0.167