Question

Snow White recieves a basket of 11 apples, out of which 3 of them are poisoned. She decides to eat 5 of them. Let X1denote the number of unpoisoned apples that she eats.
Check all that are true about X1.
A. The trials are independent
B. The trials have two outcomes
C. The trials have the same probability of success.
D. There are a set number of trials
E. We can model X1 with a collection of trials

Snow White recieves an unlimited basket of apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She makes the questionable choice to keep eating them until she eats a poisoned one. Let X2 denote the number of unpoisoned apples that she eats.
Check all that are true about X2.
A. The trials have two outcomes
B. We can model X2 with a collection of trials
C. The trials have the same probability of success.
D. The trials are independent
E. There are a set number of trials

Snow White recieves a basket of 5 apples, all of whom are either poisoned or not. There is a 0.4 chance they are poisoned. She decides to eat all of them. Let X3 denote the number of unpoisoned apples that she eats.
Check all that are true about X3.
A. The trials have two outcomes
B. There are a set number of trials
C. We can model X3 with a collection of trials
D. The trials have the same probability of success.
E. The trials are independent

Snow White recieves a basket of 5 apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She decides to eat all of them. Let X4 denote the number of unpoisoned apples that she eats.
Check all that are true about X4.
A. The trials are independent
B. We can model X4 with a collection of trials
C. The trials have the same probability of success.
D. There are a set number of trials
E. The trials have two outcomes

Which of the following are a binomial random variable?
A. X2
B. X4
C. X3
D. X1

Answer 1

For X1:

Since apples are drawn without replacement so trials are not independent. Since trials are not independent so probability of success is not same for each trial. Each trial has only two outcomes : unpoisoned and poisoned

Number of trials is fix and equal to 5.

So correct option is:

B. The trials have two outcomes
D. There are a set number of trials

E. We can model X1 with a collection of trials

Note: It can be modeled as hypergeometric distribution.

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For X2:

A. The trials have two outcomes
B. We can model X2 with a collection of trials
C. The trials have the same probability of success.
D. The trials are independent

Note: It can be modeled as geometric distribution.

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For X3:

A. The trials have two outcomes
B. There are a set number of trials
C. We can model X3 with a collection of trials
D. The trials have the same probability of success.
E. The trials are independent

Note: It can be modeled as binomial distribution.

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For X4:

A. The trials are independent
B. We can model X4 with a collection of trials
C. The trials have the same probability of success.
D. There are a set number of trials
E. The trials have two outcomes

Note: It can be modeled as binomial distribution.

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Which of the following are a binomial random variable?
B. X4
C. X3