Question

For each of the following situations, explain whether the binomial distribution applies for X.

a. You are bidding on four items available on eBay. You think that you will win the first bid with probability 25% and the second through fourth bids with probability 30%. Let X denote the number of winning bids out of the four items you bid on.

b. You are bidding on four items available on eBay. Each bid is for $70, and you think there is a 25% chance of winning a bid, with bids being independent events. Let X be the total amount of money you pay for your winning bids.

Answer 1

Solution: The conditions necessary for any random experiment to be binomial is given below:

• The experiment consists of n repeated trials.
• Each trial can result in just two possible outcomes.
• The probability of success, denoted by P, is the same on every trial.
• The trials are independent

Now let's consider part a

a. You are bidding on four items available on eBay. You think that you will win the first bid with probability 25% and the second through fourth bids with probability 30%. Let X denote the number of winning bids out of the four items you bid on.

Answer:

We have here:

Fixed number of trials i.e., 4.

Each trial has two possible outcomes.

The probability of success, denoted by P, is not same on every trial.

Also the events are not indpendent.

Hence, the random experiment under part a is not binomial experiment.

b. You are bidding on four items available on eBay. Each bid is for $70, and you think there is a 25% chance of winning a bid, with bids being independent events. Let X be the total amount of money you pay for your winning bids.

Answer: Here we have:

Fixed number of trials i.e., 4

Each trial has two possible outcomes.

The probability of success, denoted by P, is same on every trial.

Also the events are indpendent.

Hence, the random experiment under part b is binomial experiment.