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

Step-by-step explanation:

Given: Total batteries = 10

Batteries that are still working = 6

Number of ways to pick 3 working batteries = $^6C_3=\dfrac{6!}{3!3!}$

$=\dfrac{6\times5\times4\times3!}{6\times3!}\\\\=20$

Number of ways of pick 3 batteries out of 10 =

$^{10}C_3=\dfrac{10!}{3!7!}=\dfrac{10\times9\times8\times7!}{6\times7!}\\\\=120$

Required probability = $\dfrac{20}{120}=0.167$

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