Mathematics: In a large bag of marbles, 20% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? (Assume this is Binomial)

In a large bag of marbles, 20% of them are red. A

serellehunt

21.01.2022

0.0256

Step-by-step explanation:

Assuming a binomial model, with probability of success (getting a red marble) p = 0.20. The probability of obtaining 'k' successes in 'n' trials is:

$P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}$

For k = 3 red marbles in n = 4 trials:

$P(x=3)=\frac{4!}{(4-3)!3!}*0.20^3*(1-p)^{4-3}\\P(x=3)=4*0.20^3*0.8\\P(x=3) = 0.0256$

The probability that the child gets exactly three red marbles is 0.0256.

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