Problem 2E

A die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up.

a. Find a sample space for this experiment.

b. Find P (odd number).

c. If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, would this change the sample space? Explain.

d. If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, would this change the value of P(odd number)? Explain.

Solution 2E

Step1 of 3:

We have A six faces Die and it has the number 1 painted on three of its faces.

The number 2 painted on two of its faces and the number 3 painted on one face.

We need to find,

a).Find a sample space for this experiment.

b).Find P (odd number).

c).If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, would this change the sample space? Explain.

d).If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, would this change the value of P(odd number)? Explain.

Step2 of 3:

a).

Let us Assume that each face is equally likely to come up.

Number 1 = 3 faces

Number 2 = 2 faces

Number 3 = 1 faces

The sample space for this experiment is S = {number1, number2, number3}

S = {1, 2, 3}.

b).

The probability that the odd numbers is given by

P(odd numbers) = P(1) + P(3)

= +

=

=

=

= .

Hence, P(odd numbers) = ⅔.

Therefore, The probability that the odd numbers is ⅔.

Step3 of 3:

c).

No, The set of possible outcomes is still {1, 2, 3}.

d).

Yes, a list of equally likely outcomes and the outcomes are = {1, 1, 1, 2, 2, 3, 3}.

so,

P(odd numbers) = P(1) + P(3)

= +

=

=

Hence, P(odd numbers) =

Therefore, The probability that the odd numbers is .

Conclusion:

Therefore,

a).The sample space for this experiment is S = {1, 2, 3}.

b).The probability that the odd numbers is ⅔.

c).The set of possible outcomes is still {1, 2, 3}.

d).The probability that the odd numbers is .