Question

Suppose that you flip a coin 11 times. What is the probability that you achieve at least 4 tails?

A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added. If this is true, what is the probability of each of the following:

A. One out of the next four cars needs oil.

Probability =

B. Two out of the next eight cars needs oil.

Probability =

C. 10 out of the next 40 cars needs oil.

Probability =

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 13% of voters are Independent. A survey asked 26 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent?

Probability =

B. What is the probability that fewer than 5 are Independent?

Probability =

C. What is the probability that more than 2 people are Independent?

Probability =

Answer 1

1.

Here, assuming that the coin is unbiased, the experiment can be considered to be a Binomial experiment, with No. of trials (n) = 11 and probability of getting a tail (p) would be 0.5.

Using probability mass function of a binomial random variable X,

To find :

= 0.8867

2.

p = 1 / 5 = 0.20

A. One out of the next four cars needs oil.

= 0.4096

Probability = 0.4096

B. Two out of the next eight cars needs oil.

= 0.2936

Probability = 0.2936

C. 10 out of the next 40 cars needs oil.

= 0.1075

Probability = 0.1075

3.

For p = 0.13 and n = 26:

A. Probability that none of the people are Independent

= 0.0267

Probability =0.0267

B. Probability that fewer than 5 are Independent

= 0.7565

Probability = 0.7565

C. Probability that more than 2 people are Independent

= 0.6751

Probability = 0.6751