Download (2 points) Each event can occur in the given number of ways. Find

(2 points) Each event can occur in the given number of ways. Find the numbers of ways all the events can
occur.
1. Event A: 6 ways
Event B: 7 ways
Event C: 4 ways
(3 points) For the given configuration, determine how many different computer passwords are possible if
digits and letters can be repeated.
2. 2 digits followed by 5 letters
1
1
A
A
A
A
A
(3 points) For the given configuration, determine how many different computer passwords are possible if
digits and letters cannot be repeated.
3. 4 letters followed by 4 digits
A A A A 1 1 1 1
(4 points each) Evaluate. Show your process.
4.
5.
6.
7.
(4 points) Find the number of distinguishable permutations of the letters in the word.
8. LETTERS
(4 points each) Find the number of possible 5-card hands that contain the cards specified. The cards are taken
from a standard 52-card deck.
9. 2 aces and three cards that are not aces
10. 5 black cards
(6 points) Use the binomial theorem to write the binomial expansion.
11.
The sixth row of Pascal’s Triangle: 1 6 15 20 15 6 1
(4 points) Find the coefficient of
in the expansion.
12.
(4 points each) You have an equally likely chance of choosing any integer from 1 through 80. Find the
probability of the given event.
13. An odd number less than 70 is chosen
There are 35 odd numbers less than 70
14. A perfect cube is chosen
There are 4 perfect cubes between 1 and 80: 1, 8, 27, 64
(4 points) Complete.
15. At a car lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of keys to one of the
cars. What are the odds in favor of choosing a set of keys to a red car?
Odds in favor is number of favorable outcomes divided by number of unfavorable outcomes
(2 points) Find
16.
.
(4 points each) Find the indicated probability. State whether A and B are disjoint events.
17.
P(A and B) is not 0 so A and B are not disjoint
18.
P(A and B) is 0 so A and B are disjoint
(4 points each) Two six-sided dice are rolled. Find the probability of the given event.
19. The sum is neither 5 nor 9
20. The sum is greater than 9
(3 points) Events A and B are independent. Find the indicated probability.
21.
(3 points) Events A and B are dependent. Find the indicated probability.
22.
(4 points each) Let n be a randomly selected integer from 1 to 40. Find the indicated probability.
23. n is 32 given that it is greater than 25
There are 15 integers greater than 25 and less than or equal to 40
24. n is prime given that it is odd
There are 20 odd numbers between 1 and 40
There are 11 prime odd numbers between 1 and 40
(4 points) Find the probability of drawing the given cards from a standard deck of 52 cards with replacement.
25. A jack, then a 7
The events are independent
(4 points) Find the probability of drawing the given cards from a standard deck of 52 cards without
replacement.
26. 2 hearts
The events are dependent
(10 points) A binomial experiment consists of n trials probability p of success on each trial. Draw a histogram
of the binomial distribution that shows the probability of exactly k successes. Describe the distribution as
either symmetric or skewed. Then find the most likely number of successes.
27.
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Skewed
0
1
2
3
4
5
6
5 successes is the most likely
(6 points) Complete.
28. According to a medical study, 40% of the people taking an experimental drug will experience an adverse side
effect within one hour after taking the drug. 15 people participated in the study.
a. What is the most likely number of people experiencing an adverse side effect?
6 people is the most likely number of people experiencing an adverse side effect
b. What is the probability at most 6 people experience an adverse side effect?