Question

Find Probability

There are 20 computers in a store. Among them, 15 are new and 5 are refurbished, but these are indistinguishable. Six computers are selected at random from the store and purchased from lab. Compute the probability that among the chosen computers, two are refurbished.

Answer 1

2/6=1/3 is the probability

Answer 2

The probability that among the 6 chosen computers, 2 are refurbished is 0.352.

Given,

Total Computers = 20

New Computers = 15

Refurbished Computers = 5

Computers selected = 6

To Find,

The probability that among the chosen computers, 2 are refurbished

Solution,

Total number of ways in which computer can be selected = Sample space

Sample space = ⁿCr = $\frac{n!}{r!(n-r)!}$

where n is the number of computers available to select from

and r is the number of computers selected

Sample Space = ²⁰C₆

Sample Space = $\frac{20!}{6! * 14!}$

Sample Space = $\frac{20*19*18*17*16*15*14!}{6! * 14!}$

Sample Space = $\frac{20*19*18*17*16*15}{6*5*4*3*2*1}$

Sample Space = 38760

If 2 computers are refurbished, 4 are new

Thus, we need to select 2 from 5 refurbished and 4 from 15 new ones

⇒ ⁵C₂ x ¹⁵C₄

⇒ $\frac{5!}{3!2!} * \frac{15!}{11!4!}$

⇒ $\frac{5*4*3!}{2!*3!} * \frac{15*14*13*12*11!}{11!*4!}$

⇒ $\frac{5*4}{2} * \frac{15*14*13*12}{4*3*2*1}$

⇒ 10 * 1365

⇒ 13650

Probability = $\frac{Event }{Sample Space}$

Probability = $\frac{13650}{38760}$

Probability = 0.352

Hence, the probability of the event occurring is 0.352.

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