Among 27 external speakers, there are three defectives. An inspector examines 7 of these speakers.
Find the probability that there are at least 2 defective speakers among the 7
(round off to second decimal place).

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Step-by-step explanation:

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fichoh fichoh · Answer 2 · 2021-10-08T13:19:21+02:00

The probability of randomly selecting atleast 2 defective speakers from 7 trials is 0.18

The probability of randomly selecting a defective speaker can be calculated thus :

P(defective) = number of defective speakers / total speakers

P(defective) = 3 / 27 = 0.1111

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)
Probability of success, p = 0.1111
n = number of trials = 7
x ≥ 2
q = 1 - p = 1 - 0.1111 = 0.889

P(x ≥ 2 ) = P(x = 2)+P(x = 3)+P(x = 4)+P(x = 5)+P(x =6)+P(x = 7)

Using a binomial probability calculator to save time :

P(x ≥ 2 ) = 0.17785

P(x ≥ 2 ) = 0.18 ( 2 decimal places)

Therefore, the probability of selecting atleast 2 defective speakers from 7 is 0.18

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Among 27 external speakers, there are three defectives. An inspector examines 7 of these speakers. Find the probability that there are at least 2 defective speakers among the 7 (round off to second decimal place).

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Among 27 external speakers, there are three defectives. An inspector examines 7 of these speakers.
Find the probability that there are at least 2 defective speakers among the 7
(round off to second decimal place).