For each of the following situations, explain whether the binomial distribution applies for x. a. You are bidding on four items available on an online shopping site. You think that you will win the first bid with a probability of 25% and the second through fourth bids with probability 30%. Let x denote the number of winning bids of the four items you bid on. b. You are bidding on four items available on an online shopping site. 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.

(a) No, the binomial distribution does not applies to the scenario because each trial does not have the same probability of success.

(b) No, the binomial distribution does not applies to the scenario because x does not count the number of successes.

Step-by-step explanation:

Binomial distribution illustrates the probability of success or failure of any result of an experiment under study which is usually repeated several trials. If we cannot predict before head, the outcome of an experiment, the experiment is called a random experiment.

Binomial experiments are random experiment with fixed number of repeated trials. For example, let consider a random experiment in which a fair coin and a fair die are tossed together. We may wish to find the probability of a head and a 5 showing up in a single throw.

The event of a head and a 5 may be considered as a combination of two events:

the event E₁ of a head showing up in the throw of the coin and; the event E₂ of a 5 showing up in the throw of die.

The event E₁ of a head showing up in the throw of the coin does not in any way affect the event E₂ of a 5 showing up in the throw of die.

We say that the event E₁ and E₂ are independent, as such the outcome in one trial has no effect on the outcome in other trials.

In binomial distribution; we are concerned with two main variables;

the number of time an experiment runs. the probability of a specific outcome

From the information given in the question: The objective of the question from both a and b is to determine if the binomial distribution applies to the scenario in both a and b?

SO;

In (a), given that:

You think that you will win the first bid with a probability of 25%;

The second through fourth bids with probability 30%.

Does the binomial distribution applies to this scenario?

No, the binomial distribution does not applies to the scenario because each trial does not have the same probability of success.

In (b); given that:

Each bid is for $70, and you think there is a 25% chance of winning a bid,

with bids being independent events. Does the binomial distribution applies to this scenario?

No, the binomial distribution does not applies to the scenario because x does not count the number of successes.