Question

A)The life expectancy in the United States has a mean of 75 with a standard deviation of 7 years and follows a normal distribution.

What is the probability of an individual living longer than 80 years?

b)In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.

What is the probability that UTC will defeat Furman given that they defeat Marshall?

c) In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.

Are the outcomes of the games independent? Explain and given reasoning for your answer.

What is the probability that UTC will win Furman or Marshall?

Answer 1

Question A

Given that the life expectancy in the United States has a mean of 75 with a standard deviation of 7 years and follows a normal distribution.

Let,

X = Life expectancy in the United States

Now we need to find the probability of an individual living longer than 80 years.

Now we know that,

Coming back to our problem,

We need to find the probability of an individual living longer than 80 years.

Hence the probability that an individual living longer than 80 years is 0.2389

Question B

Given that in the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55.

Let,

Therefore,

Now it is also given that the probability that UTC will defeat both opponents is 0.3465.

Here we need to find the probability that UTC will defeat Furman given that they defeat Marshall.

Before we go on to solve the problem let us know a bit about conditional probability.

Conditional Probability

Given two events A and B. Now the probability that B occurs given that A had already occured is given by,

Coming back to our problem

We need find the probability that UTC will defeat Furman given that they defeat Marshall.

Hence the probability that UTC will defeat Furman given that they defeat Marshall 0.55

Question C

Given that in the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55.

Let,

Therefore,

Now it is also given that the probability that UTC will defeat both opponents is 0.3465.

Here we need to see if the outcomes of the games are independent.

Before we go on to solve the problem let us know a bit about independent events.

Given two events A and B. Now this two events A and B are said to be independent if,

Coming back to our problem

Now,

Hence the outcomes of the games are independent.

Now we need find the probability that UTC will win Furman or Marshall.

We know that,

Hence the probability that UTC will win Furman or Marshall is 0.8335