For problems #1-5 you are picking one card from a standard deck of \(52\) playing cards, find each probability.
1) P(red ace)
2) P(face card)
3) P(even number)
4) P(ace of diamonds)
5) P(a multiple of four)
For problems #6-10 use the following diagram that gives all the possible ways to roll two dice together.
1) P(red ace)
2) P(face card)
3) P(even number)
4) P(ace of diamonds)
5) P(a multiple of four)
For problems #6-10 use the following diagram that gives all the possible ways to roll two dice together.
Suppose you roll two dice together. Find the following probabilities.
6) What is the most likely sum to roll? How likely is it?
7) What is the probability of rolling at least a \(9\)?
8) What is the probability of rolling a prime sum?
9) What is the probability of not rolling a sum of \(2\)?
10) What is the probability of a \(3\) showing up on at least one of your dice?
For problems #11-15 there are \(42\) people in the jury pool, \(25\) of which are female and \(17\) of which are male. A jury consists of \(12\) people.
11) Find the probability that a jury selected from the pool contains exactly \(6\) men and \(6\) women.
12) Find the probability that a jury selected from the pool contains less than \(3\) men.
13) Find the probability that a jury selected from the pool consists of entirely the same gender.
14) Find the probability that a jury selected from the pool contains at least one man.
15) What do you think the most likely makeup of jurors is in this situation? Explain your reasoning.
For problems #16-20 find the probabilities from the given information.
There is a class of \(30\) students, \(15\) are juniors, \(12\) are sophomores, and the rest are freshmen. There are \(16\) girls and \(14\) boys in the class. There are \(21\) students in the class that participate in a school sport. There are \(13\) students in the class that participate in a non-athletic extracurricular activity. There are \(8\) students that participate in both a sport and a non-athletic extracurricular activity. Two freshmen do not play a sport. Half of the sophomores are girls, \(\dfrac{2}{5}\) of the juniors are boys.
16) Find the probability that one randomly selected student is either a junior or a freshmen.
17) Find the probability that one randomly selected student is in a sport or a non-athletic extracurricular activity.
18) Find the probability that one randomly selected student is girl or is a sophomore.
19) Find the probability that one randomly selected student is a freshmen or plays a sport.
20) Find the probability that one randomly selected student is a junior or a boy.
For problems #21-25 use the following information.
A bag of marbles contains \(50\) marbles. \(18\) are green, \(20\) are red, \(6\) are orange, \(4\) are pink, and \(2\) are yellow.
21) If you pick out one marble, find P(green or red).
22) If you pick out two marbles without replacement, find P(pink and then yellow).
23) If you pick out two marbles with replacement, find P(red and orange).
24) If you pick out one marble, find P(red | red).
25) If you pick out one marble, find P(pink | green).
26) You survey the senior class at the end of first semester and find out that \(82\%\) have applied to at least one college. Of those that have applied, \(15\%\) are confident about what they want their career to be. Of those that have not applied, \(9\%\) are confident about what they want their career to be. What percent of students in the senior class are confident about what they want their career to be?
27) If there are \(5\) friends that line up in a random order, what is the probability that they lined up in exact order of age?
28) On the list of top \(50\) selling albums of all time, The Beatles have three albums. If you randomly select \(10\) albums off the list, what is the probability that you selected all three Beatles albums?
29) In a lottery, there are \(48\) numbers that can be picked, and numbers cannot be repeated. \(6\) numbers are selected to find a winner. The grand prize is given to anyone whose ticket has all \(6\) numbers in any order. If you buy one ticket, find the probability that you will win the grand prize.
30) Follow up question to #29: If each ticket costs 1 dollar and the grand prize is \(\$2,000,000\), does it make sense to buy one ticket for this lottery?
Review
31) Evaluate without a calculator \(\cos (\large\frac{\pi}{3})\).
32) If you deposit \(\$1000\) into an account that earns \(100\%\) interest compounded continuously, how much money will you have in your account after 1 year?
33) What is the range of \(f(x)=2 \log x\)?
34) If a pendulum swings through an initial arc of \(4\) feet and its swing shortens by \(3\%\) after each swing, how many feet has the pendulum swung through when it comes to a complete stop?
35) Who is the number \(e\) named for?
Solution Bank
6) What is the most likely sum to roll? How likely is it?
7) What is the probability of rolling at least a \(9\)?
8) What is the probability of rolling a prime sum?
9) What is the probability of not rolling a sum of \(2\)?
10) What is the probability of a \(3\) showing up on at least one of your dice?
For problems #11-15 there are \(42\) people in the jury pool, \(25\) of which are female and \(17\) of which are male. A jury consists of \(12\) people.
11) Find the probability that a jury selected from the pool contains exactly \(6\) men and \(6\) women.
12) Find the probability that a jury selected from the pool contains less than \(3\) men.
13) Find the probability that a jury selected from the pool consists of entirely the same gender.
14) Find the probability that a jury selected from the pool contains at least one man.
15) What do you think the most likely makeup of jurors is in this situation? Explain your reasoning.
For problems #16-20 find the probabilities from the given information.
There is a class of \(30\) students, \(15\) are juniors, \(12\) are sophomores, and the rest are freshmen. There are \(16\) girls and \(14\) boys in the class. There are \(21\) students in the class that participate in a school sport. There are \(13\) students in the class that participate in a non-athletic extracurricular activity. There are \(8\) students that participate in both a sport and a non-athletic extracurricular activity. Two freshmen do not play a sport. Half of the sophomores are girls, \(\dfrac{2}{5}\) of the juniors are boys.
16) Find the probability that one randomly selected student is either a junior or a freshmen.
17) Find the probability that one randomly selected student is in a sport or a non-athletic extracurricular activity.
18) Find the probability that one randomly selected student is girl or is a sophomore.
19) Find the probability that one randomly selected student is a freshmen or plays a sport.
20) Find the probability that one randomly selected student is a junior or a boy.
For problems #21-25 use the following information.
A bag of marbles contains \(50\) marbles. \(18\) are green, \(20\) are red, \(6\) are orange, \(4\) are pink, and \(2\) are yellow.
21) If you pick out one marble, find P(green or red).
22) If you pick out two marbles without replacement, find P(pink and then yellow).
23) If you pick out two marbles with replacement, find P(red and orange).
24) If you pick out one marble, find P(red | red).
25) If you pick out one marble, find P(pink | green).
26) You survey the senior class at the end of first semester and find out that \(82\%\) have applied to at least one college. Of those that have applied, \(15\%\) are confident about what they want their career to be. Of those that have not applied, \(9\%\) are confident about what they want their career to be. What percent of students in the senior class are confident about what they want their career to be?
27) If there are \(5\) friends that line up in a random order, what is the probability that they lined up in exact order of age?
28) On the list of top \(50\) selling albums of all time, The Beatles have three albums. If you randomly select \(10\) albums off the list, what is the probability that you selected all three Beatles albums?
29) In a lottery, there are \(48\) numbers that can be picked, and numbers cannot be repeated. \(6\) numbers are selected to find a winner. The grand prize is given to anyone whose ticket has all \(6\) numbers in any order. If you buy one ticket, find the probability that you will win the grand prize.
30) Follow up question to #29: If each ticket costs 1 dollar and the grand prize is \(\$2,000,000\), does it make sense to buy one ticket for this lottery?
Review
31) Evaluate without a calculator \(\cos (\large\frac{\pi}{3})\).
32) If you deposit \(\$1000\) into an account that earns \(100\%\) interest compounded continuously, how much money will you have in your account after 1 year?
33) What is the range of \(f(x)=2 \log x\)?
34) If a pendulum swings through an initial arc of \(4\) feet and its swing shortens by \(3\%\) after each swing, how many feet has the pendulum swung through when it comes to a complete stop?
35) Who is the number \(e\) named for?
Solution Bank