A collection of 22 laptops includes 6 defective laptops. If

Sabrina Waller

Sabrina Waller

Answered question

2022-02-09

A collection of 22 laptops includes 6 defective laptops. If a sample of 3 laptops is randomly chosen from the collection, what is the probability that at least one laptop in the sample will be defective?

Answer & Explanation

Keely House

Keely House

Beginner2022-02-10Added 13 answers

Step 1
The likelihood that a laptop is broken is (622)
The likelihood that a laptop won't have a problem is(1622)
The probability that at least one laptop is defective is given by:
P(1 defective)+P(2 defective)+P(3 defective)
as this probability is cumulative. Let X be the number of laptops found to be defective.
P(X=1)=(3 choose 1)(622)1×(1622)2=0.43275
P(X=2)=(3 choose 2)(622)2×(1622)1=0.16228
P(X=3)=(3 choose 3)(622)3=0.02028
(Sum up all of the probabilities)
=0.615310.615

hotlegsaprile2u

hotlegsaprile2u

Beginner2022-02-11Added 21 answers

Step 1
P(X1), N=22, K=6, n=3
P(X1)=P(1X3)=1P(X0)=1(P(X=0))
P(X=0)=(K0)(NKn0)(Nn)
=(60)(22630)()=(60)(163)(223)
=1×5601540=5601540=411
=0.363636
Answer: =1(0.363636)=0.636364

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