1A) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a
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Question
1A) 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, three green ones, fourwhite 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 red ones.
1B) 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, threewhite 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 green ones.
Explanation / Answer
Solution:-
To find the probability that she does get all the red ones, we must find two values: the total number of possible outcomes, , and the total number of favorable outcomes for the given event (getting all the red marbles). Since she is choosing 8 marbles from a total of 12, = (12, 8) = 495. To get all the red ones, she must choose 4 red from 4, and then choose the remaining 4 marbles from the 8 non-red ones. There are (4,4)(8, 4) = 70 ways to do this. Thus, probability = 70/ 495 .
The probability of not occurring is then = 1 - 70/ 495 = 425 / 495 = 85/99 , so this is the probability that she does not get all the red ones.
(b) To find the probability that she does get all the green ones, we must find two values: the total number of possible outcomes, and the total number of favorable outcomes for the given event (getting all the green marbles).
Since she is choosing 8 marbles from a total of 13, is (13, 8) = 1287. To get all the green ones, she must choose 4 green from 4, and then choose the remaining 4 marbles from the 9 non- green ones. There are (4,4) * (9, 4) = 126 ways to do this. Thus, probalility = 126/1287.
The probability of ?? not occurring is then = 1 ? 126/ 1287 = 1161 / 1287 = 129/143 , so this is the probability that she does not get all the green ones.
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