Question

A) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She has all the red ones.

B) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She does not have all the red ones.

C) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She does not have all the green ones.

Answer 1

A.

Let S be the sample space and E be the event that she gets all the reds.

Since she is choosing 8 marbles from a total of 12, ?(?) = ?(12, 8) = 495

n(E) = C(4,4)*C(8,4) = 70

P(E) = 70/495

= 0.1414

B.

P(she does not have all the red ones) = 1-P(E)

= 1 - 0.1414

= 0.8586

C.

Let S be the sample space and E be the event that she gets all the greens.

Since she is choosing 8 marbles from a total of 12, ?(?) = ?(12, 8) = 495

n(E) = C(2,2)*C(10,6) = 210

P(E) = 210/495

= 0.4242

P(She does not have all the green ones) = 1-P(E)

= 0.5758

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