A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. if three of the products are randomly selected, find the probability that all of them are acceptable.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of all the three products being selected is 0.343.

What is Binomial distribution?

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

The probability of accepting a product is 0.7(70%), while rejecting is 0.3(30%). Therefore, using the binomial distribution the probability of all the tree products being selected is,

P(X=3) = ³C₃ (0.7)³ (0.3)⁽³⁻³⁾

= 1 × 0.343 × 1

= 0.343

Hence, the probability of all the three products being selected is 0.343.

Learn more about Binomial Distribution:

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