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Preview File Edit View Go Tools Window Help a Thu 1:50 PM a 89% s Homework 2.pdf (page 1 of 2) Q Search probability 0.75. In the event there is no volleyball, David will not attend Arman and Vinayak's party with a probability of 0.2. 2.pdf a) b) c) d) Represent this situation with a tree diagram. Label the parts clearly What is the probability there is no volleyball? What is the probability David attends Arman and Vinayak's party? Assuming David did not attend the party, what is the probability there was volleyball at the party? A campus singing group, "The Whole Notes", will have 12 members and is holding auditions. Suppose that there are 25 people auditioning to be in "The Whole Notes. Fifteen of those auditioning are women. 3. a) b) c) d) e) How many ways can the singing group be formed from among these 25 people? What is the probability that the singing group will be evenly split between men and women? What is the probability that at least 2 men will be in the singing group? What is the probability that the singing group will be all female? Suppose that the singing group, there will be 3 sopranos, 4 altos, 3 tenors, and 2 basses. Of the 25 people auditioning to be in the group, 9 are sopranos, 8 are altos, 6 are tenors and the rest are basses. How many ways are there to form "The Whole Notes"? All 25 singers are asked to take a written music theory test. The top 6 scorers will be ranked (regardless of vocal part). How many possible rankings of the top 6 are there from among all the singers? f) Luke Skywalker is shopping for a new lightsaber because he lost his in an accident. The lightsaber store has 6 blue, 5 green, and 3 red lightsabers in stock on their shelf. The lightsabers are all identical except for color 4. Items: 6696 Unread: 1616 All folders are up to date. Connected to: Purdue 1616 21Explanation / Answer
(a)
There are total 25 people came for audition and 12 need to be selected. This can be done in 25C12 ways = 5200300
(b)
There are 15 Women and 10 Men in 25 people who came for audition.
For even split 6 women and 6 men are to be selected, this can be done in 15C6 * 10C6 = 1051050 ways
Required probability = 15C6*10C6/25C12 = 0.2021
(c)
Consider less than 2 men in singing group, this can be done in 10C1*15C11 + 10C0*15C12 = 14105
Required probability = 1 - 14105/5200300 = 0.997287656
(d)
All female can be selected in 15C12 ways = 455
Required probability = 455/5200300 = 0.0000875
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