Question

For a subject making random guesses for each answer on a 4 question quiz, the probabilities for the number of correct responses are given in the table:

x	P(x)
0	0.4096
1	0.4096
2	0.1536
3	0.0256
4	0.0016

Is the given probability distribution a valid probability distribution? Explain why or why not.

Find the probability of getting at least one correct answer.

Find the probability that the number of correct answers is 2 or 3.

There is a 6% delinquency rate for consumers with a good credit rating score. If the JP Morhan Bank gives loans to 60 people with good credit scores, what is the probability that exactly one of them becomes delinquent?

Answer 1

Q 1)

a)

Is the given probability distribution a valid probability distribution? Explain why or why not.

For any probability distribution to be valid, the condition is the total probability must be equal to 1.

Here in our case, the total probability is = 0.4096+0.4096+ 0.1536+ 0.0256+0.0016 = 1

Hence,the given probability distribution is a valid probability distribution.

b)

Find the probability of getting at least one correct answer.

c)

Find the probability that the number of correct answers is 2 or 3.

Since the outcomes are mutually disjoint, the probability is :