Probability Test Review
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#1-3. There are 15 people in Mrs. Denney’s 2nd period class, 10 boys and 5 girls.
1. How many ways can she choose 4 boys to carry something to the office?
2. How many ways can she line all 5 girls up in the front of the class?
3. How many ways can she pick 3 students to do the following things: create a
bulletin board, make copies, and take something to ISS?
4. You draw a card from a standard deck of cards. What is the sample space of
possible suits?
#5-9. You throw a dart at the board.
5. What is the probability of landing in the red circle
(shaded)?
6. What is the probability that two darts in a row land in the
red circle (shaded)? What about 8 in a row?
7. If you pay $5 to play and win $15, is it a fair game? Explain.
8. Should you play? Explain.
9. If you choose a card at random from a well-shuffled deck of 52 cards, what is
the probability that the card chosen is a spade? Not a spade?
10.Which of the following pairs of events are disjoint?
A:
A:
A:
A:
A:
The even numbers;
B:
the even numbers;
B:
the numbers greater than 5; B:
the numbers above 100;
B:
negative numbers;
B:
the number 5
the numbers greater than 10
all negative numbers
all negative numbers
odd numbers
Use the following information for #11-13. The suit of 13 diamonds (A, 2 to 10,
J, Q, K) from a standard deck of cards is placed in a hat. The cards are
thoroughly mixed and a student reaches into the hat and selects two cards
without replacement.
11. What is the probability that the first card selected is the ace?
12. Given that the first card selected is the ace, what is the probability that the
second card is the two?
13.What is the probability of selecting the ace on the first draw and then the 2?
14. On a normal die, what is the probability that you roll an even number or a 3?
15. On a normal die, what is the probability that you roll an even number or a
multiple of 3?
16.In a math class, 70% of the students are in a club and 30% play a sport. If
15% of the students are in a club and play a sport, what is the probability that
a randomly selected student is in a club or plays a sport?
#17-19. Suppose you the probability of a student not coming to school on a
Monday is 0.07. The probability of a student not coming to school on a Friday is
0.15. The probability that a student will not come to school on both Monday and
Friday is 0.04.
17.Are the events not coming to school on Monday and not coming to school on
Friday independent? Show work to support your yes/no answer.
18.What is the conditional probability of not coming to school on Monday given you
did not come to school on Friday?
19.What is the probability of not coming to school on Monday or Friday?
20. A candy store has a jar on the counter that contains lollipops. The owner of
the store places 10 red lollipops, 5 green lollipops, 5 yellow lollipops and 5 orange
lollipops in the jar every morning. Every child can take one free lollipop before
leaving the store. Assuming the first child chose a red lollipop, what is the
theoretical probability that the second child will choose a red lollipop?
#21-27- Use the given Venn Diagram.
21. How many students are taking a foreign
language?
22. How many students play a sport?
23. How many students do both?
24. How many students do not play a sport
and do not take a foreign language?
25. How many students play a sport but do not take a foreign language?
26. How many students were polled?
27. Organize the information into a two way table.
Play a sport
Do not play a sport
Take a foreign
14
23
language
Do not take a
foreign language
Total
Total
37
50
#28-31. A class was surveyed about whether they have been to Canada or
Mexico.
28. Find the probability that a student has been to Canada.
29. Find the probability that a student has been to Canada given they have been
to Mexico.
30. Find the probability that a student has been to Canada and been to Mexico.
31. Are the events “been to Canada” and “been to Mexico” independent? Show
work to justify your answer.