6. Ten different boys are auditioning for a play. The directors are looking to cast only three of the boys. If three of the boys were chosen at random, then what is the probability that all three of the boys chosen are the brothers? Show your answer in fraction and percent, round to the nearest thousandth.

If a card is pulled from a deck of playing cards and a six-sided die is tossed, then what is the probability that the following two independent events will occur?

7. Rolling an odd number and drawing a King.

8. Drawing a 10, and rolling an odd number.

If a dice is rolled and the spinner below with 5 sides, each with the letters A, B, C, D, E is spun, then what is the probability of the following independent events occurring at the same time?

9. Spinning a vowel.

10. Spinning a vowel and rolling an even number.

Identical dials are spun, each dial contains X, Y, and Z. What is the probability that:

11. Four identical spinners would all land on either Y or Z?

12. Five identical spinners would all land on X?

A dealer holds a shuffled deck of 52 playing cards and draws cards at random. Determine the probability that the following events would occur, without replacement.

13. The first card drawn is a spade.

14. The first card dealt is the ace of spades.

15. Six different numbers are drawn separately on 11 different cards, one number on each card. There is one 1, three 2's, two 3's, three 4's, one 5, and one 6. Two cards are drawn in a row with replacement. What is the probability that neither of them is a 4?

16. Let's say that a piece of dice is rolled four times, and we are looking for how many times a 5 will be rolled. Determine the probabilitypthat a 5 will be rolled.

17. Let's say that a piece of dice is rolled four times, and we are looking for how many times a 5 will be rolled. Determine the probabilityqthat anything besides a 5 will be rolled.

18. Let's say that a piece of dice is rolled seven times. Write the expansion in the binomial distribution form to represent the possibility of rolling exactly five 3's.

19. Find P(3) if n=5 and p = 1/5

20. Find the following values for p, q, x, and n, based on P(4)= 6C⁴p⁴q²when n is equal or greater than x.

Refer to this set of data for the following questions:

Number of Heads	Frequency
0	24
1	100
2	146
3	76
4	40
5	14

21. Which column represents the range?

22. Which column represents the domain?

23. How many coins were flipped during this experiment, based on the data given?

24. How many total times were the group of coins flipped?

25. Which number of heads has the greatest frequency?

26. Which number of heads has the lowest frequency?

27. Determine the range and mean for the following set of numbers: 140, 112, 132, 166, 153, 110.

28. Find the mean and standard deviation for the following set of numbers: 40, 34, 42, 26, 28.

29. Find the mean and standard deviation for the following set of numbers: 12, 7, 13, 8.