At a carnival, the probability that a person will win a prize at the ring-toss game has been found to be zo. What is the probability that a prize will be
won by exactly
a. 1 of the next 5 players?
b. 3 of the next 5 players?
c. 0 of the next 5 players?
d. 2 of the next 20 players?

a) 0.20363

b) 0.00113

c) 0.77378

d) 0.18868

Step-by-step explanation:

Complete Question

At a carnival, the probability that a person will win a prize at the ring-toss game has been found to be (1/20). What is the probability that a prize will be won by exactly

a. 1 of the next 5 players?

b. 3 of the next 5 players?

c. 0 of the next 5 players?

d. 2 of the next 20 players?

Solution

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure.

The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 5, 20

x = Number of successes required = 1, 3, 0, 2

p = probability of success = probability of winning a prize in the ring-toss = (1/20) = 0.05

q = probability of failure = probability of NOT winning a prize in the ring-toss = 1 - (1/20) = (19/20) = 0.95

a. 1 of the next 5 players?

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 5

x = Number of successes required = 1

p = probability of success = 0.05

q = probability of failure = 0.95

P(X = 1) = ⁵C₁ (0.05)¹ (0.95)⁵⁻¹ = 0.2036265625 = 0.20363

b) 3 of the next 5 players?

n = total number of sample spaces = 5

x = Number of successes required = 3

p = probability of success = 0.05

q = probability of failure = 0.95

P(X = 3) = ⁵C₃ (0.05)³ (0.95)⁵⁻³ = 0.001128125 = 0.00113

c. 0 of the next 5 players?

n = total number of sample spaces = 5

x = Number of successes required = 0

p = probability of success = 0.05

q = probability of failure = 0.95

P(X = 0) = ⁵C₀ (0.05)⁰ (0.95)⁵⁻⁰ = 0.7737809375 = 0.77378

d. 2 of the next 20 players?

n = total number of sample spaces = 20

x = Number of successes required = 2

p = probability of success = 0.05

q = probability of failure = 0.95

P(X = 2) = ²⁰C₂ (0.05)² (0.95)²⁰⁻² = 0.18867680127 = 0.18868

Hope this Helps!!!

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.