6.4: Practice Problems
- Page ID
- 139283
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Suppose you roll a six-sided die. Determine the following:
a. P(rolling a 5)
b. P(rolling an even number)
c. \(\mathrm{P}\) (rolling a number bigger than 2 )
2. Compute the probability of tossing a six-sided die and getting a 7 .
3. Compute the probability of tossing a six-sided die and getting a number less than 3.
4. Compute the probability of rolling a 12-sided die and getting a number other than 8.
5. A test was given to a group of students. The grades and gender are summarized below.
|
A |
B |
C |
Total |
|
|
Male |
8 |
18 |
13 |
39 |
|
Female |
10 |
4 |
12 |
26 |
|
Total |
18 |
22 |
25 |
65 |
a. Find the probability that a student chosen at random was female.
b. Find the probability that a student chosen at random did NOT earn a C?'
6. The table below shows the number of credit cards owned by a group of individuals.
|
Zero |
One |
Two or more |
Total |
|
|
Male |
9 |
5 |
19 |
33 |
|
Female |
18 |
10 |
20 |
48 |
|
Total |
27 |
15 |
39 |
81 |
a. Find the probability that a person chosen at random had no credit cards.
b. Find the probability that a person chosen at random has at least one credit card?
7. A ball is drawn randomly from a jar that contains 6 red balls, 2 white balls, and 5 yellow balls. Find the probability of the given event.
a. A red ball is drawn
b. A white ball is drawn
8. A bag contains 2 gold marbles, 10 silver marbles, and 25 black marbles. You randomly select one marble from the bag. What is the probability that you select a gold marble?
9. Suppose you write each letter of the alphabet on a different slip of paper and put the slips into a hat. What is the probability of drawing one slip of paper from the hat at random and getting:
a. A consonant
b. A vowel
10. A group of people were asked if they had run a red light in the last year. 150 responded "yes", and 185 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.
11. In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dogs, and 40 indicated they don't enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats.
12. If you pick one card at random from a standard deck of 52 cards, what is the probability it will be a King?
13. If you pick one card at random from a standard deck of 52 cards, what is the probability it will be a Diamond?
14. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not the Ace of Spades?
15. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not a heart?
16. If you pick one card at random from a standard deck of 52 cards, what is the probability it will be an 8 ?
17. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not a 6 ?
18. If you pick one card at random from a standard deck of 52 cards, what is the probability it will be a face card?
19. If the probability of a certain event is \(\frac{24}{61}\), what is the probability of the event not happening?
20. If the probability of a certain event not happening is \(\frac{38}{45}\), what is the probability of the event happening?
21. Find the odds for rolling a die and getting a 1.
22. Find the odds for rolling a die and getting an even number.
23. If you pick one card at random from a standard deck of 52 cards, what are the odds it will be an ace?
24. If you pick one card at random from a standard deck of 52 cards, what are the odds it will be a face card?
25. If the probability of a certain event is \(\frac{51}{92}\), what are the odds against the event happening?
26. If the odds against a certain event are 2 to 7 , what is the probability of the event occurring?
27. If you pick one card at random from a standard deck of 52 cards, what are the odds it will not be a heart?
28. Find the odds for rolling a die and not getting a 6 .