Question

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time?

Answer 1

Step-by-step explanation:

The probability of success = 8/(8 + 17) = 8/25 = 0.32.

Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.

Hence, X ~ Bin(4, 0.32).

Thus, P(X = 1) = $4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3$

Answer 2

The probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

 

We have:

There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.

The probability of success

P = 8/(8 + 17)

P = 8/25

P = 0.32

Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.

So,

X ~ Bin(4, 0.32).

Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹

= C(4, 1)(0.32)¹ (0.68)³

Thus, the probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

Learn more about the probability here:

brainly.com/question/11234923

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