Question

Question 3 and 5.

le Stuuents in your particular class? IME 383 days in a year (ignoring leap-year birthdays and your knowledge of twins). 3. The dreidel game is a children's game of chance played during the Hanukkah holiday. One wins by collecting the most objects (e.g, nuts, candies, beans, or coins) from the pot. Players take one of four actions, depending on where the dreidel lands on their spin. A dreidel is a 4-sided top with a Hebrew letter on each of the four sides. One letter means "nothing," in which case you take nothing from the pot. Another letter means "take everything," and a third letter means "take half" (players might agree that the spinner in this case also gets the leftovers that is, half of 9 would be 5). Finally the last letter indicates that you contribute to the pot. a. If each player starts with 15 objects, what is the probability that the third player will get to pick something from the pot, assuming that prior to starting the pot was empty? b. Suppose each player had 15 objects, and the game begins with 2 objects in the pot. What is the probability that the third player will get to pick something from the pot? At a particular college, 80% of the students are aged 17-25. (There are no students under 17 here.) Older students tend to live off campus. In fact, P(17 to 25 | off campus) = 0.14 4, and P( 25 on campus) 0.06. What percent of college students live off campus? Below are three students' answers to the question in Activity 7. Conjecture what each student understands about the problem situation, sample space, and probability. Use the language of chance event, outcomes, and other probability vocabulary as appropriate. 5.

Answer 1

You have said to answer 3 and 5 but question 5 is not posted completely. Only the first 3 lines are there in image . So I will answer question 3.

3.a) Since it is not specified how many rounds the driedel is rolled by each player, I assume there is only one round .

Prior to start the pot is empty and we need the probability that the third player will get to pick something from the pot. There must be something in the pot put by either first or second player for third player t o pick. This can happen in 2 cases.

Case 1: first contributes and second do nothing  .

1/4( since 1 out of 4 sides say contribute ) *1/4

probability =1/16

Case 2: first does whatever and  second contributes= 1*1/4=1/4

Adding 1/16+1/4=5/16

Probability third player rolls take everything or take half = 2/4=1/2

required probability =5/16*1/2=5/32

3.b) Probability pot has something = 1- Probability pot will have nothing .

Pot can have nothing in 3 cases.

Case 1 : first player takes all and second does not contribute

=1/4*3/4=3/16

Case 2 : first player takes half and second rolls half or all ( both taking last one from pot)

=1/4*2/4=2/16

Case 3:First does not take any and second takes all

2/4*1/4=2/16

Adding gives 7/16

So Probability pot has something = 1- 7/16=9/16

Third player picks anything = 9/16*1/2=9/32

Thats the required probability. Its all about knowing since there are 4 rolls each first 2 people can roll a combination of 4*4 =16 combinations.

Hope you understand . Happy learning.