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Sagot :
The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.
What is the binomial probability formula?
The binomial probability formula is
P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = [tex]\frac{n!}{(n-x)!x!} p^xq^{(n-x)}[/tex]
Where n is the number of trials, p i is the probability of success, and q is the probability of failure.
And q = 1 - p
Calculation:
It is given that, a card is selected from a standard deck and replaced.
This experiment has repeated a total of five times. i.e., trials n = 5
So, the probability of success is p = 1/4 = 0.25
(Since one card is to be selected from the five trials where each time the card is replaced)
Then, the probability of failure is q = 1 - 0.25 = 0.75
And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.
Then, using the binomial probability formula, we get
P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878
On rounding off, we get the required probability as 0.088.
Learn more about the binomial probability of random variables here:
https://brainly.com/question/15246027
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