6.4: Practice Problems
- Page ID
- 139283
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
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 .