Likelihood
Twenty-five volunteers will wear one of 6 blue, 7 green, 8 yellow, and 4 red aprons during an upcoming food drive. If the aprons are assigned randomly, what is the probability that a volunteer is assigned an apron that is NOT green?
18/25
What is the formula to find the probability of an event?
P (event)= Number of Favorable Outcomes/ Total Number of Possible Outcomes
wo number cubes whose sides are numbered 1 through 6 are rolled on a table. The two numbers showing are added. If you repeat this process 300 times, how many times would you expect the two cubes to add to exactly 7?
50 times
There are four groups left to present their final projects. The groups are listed alphabetically from Group A to Group D. The teacher will choose one group at random to present their project. List all the outcomes in this sample space for this action.
Group A, Group B, Group C, Group D
Leah flips a coin, and then she spins a spinner with 3 equal sections colored red, green, and blue. What is the probability that the coin flips heads, and the spinner land on either red or blue? Write your answer as a percentage, to the nearest percent.
33%
Mr. Sullivan places tiles numbered 1 through 18 in a bag and assigns a number to represent each of the 18 students in his class. Students will present their final reports in the order that their assigned tiles are drawn from the bag. Is Mr. Sullivan being fair? Explain.
Yes: Each tile has an equal probability of being selected.
Mason plays a game by flipping two fair coins. He wins the game if both coins land facing heads up. If Mason plays 300 times, how many times should he expect to win? Explain.
75 times: The theoretical probability that both coins will land facing heads up is 1/4; 1/4 = 75/300.
A fair coin is flipped 10 times and lands on heads 8 times. Provide one reason to justify the difference between the experimental and theoretical probabilities.
Ten is not a great number of trials. With more flips of the coin, the experimental probability will likely approach the theoretical probability of 50%.
A number cube is weighted so that the faces 1,2, or 3 are all twice as likely to occur as each of the faces labeled 4,5, or 6. What statements must you add to P(1)=2/9, P(2)= 2/9, P(3)=2/9 to make a complete probability model?
P(4)=1/9
P(5)= 1/9
P(6)=1/9
A fair coin is flipped four times. Use a tree diagram to find the probability of observing exactly two heads. Write your answer as a percentage, to the nearest percent.
38%
Holly throws a 12-sided number solid with faces labeled 1 through 12. What is the probability that Holly will roll a number greater than 12?
0
Sanji throws an 8-sided sold with faces numbered 1 through 8. Select all of the true statements.
A: P(even number)= 1/8
B: P(multiple of 3)= 1/4
C: P(odd number)= 1/2
D: P(number less than 8)= 1
E: P(factor of 24)= 3/4
F: P(the number 9)= 0
B,C,E,F
Five different names were put into a hat. A name is chosen 111 times and then name Karen is chosen 28 times. What is the experimental probability of the name Karen being chosen?
28/111 or about 25%
Ashley collects colored golf balls from a miniature golf course. She will randomly select one ball from her collection of 9 blue, 7 magenta, and 2 purple golf balls.
What is the total number of colored golf balls in Ashley’s collection?
18
Faith and Shawna are shopping for shirts. The available styles are short sleeve (S), tank top (T), and long sleeve (L). Make an organized list to show all possible outcomes if each girl buys a new shirt.
(S, S), (S, T), (S, L), (T, S), (T, T), (T, L), (L, S), (L, T), (L, L)
How likely is it to rain if the chances are < 1/2?
Explain.
Unlikely: it's less that 50%
What does it mean that there is an equal theoretical probability of each outcome?
There should be a fair chance of each outcome happening
A spinner has 4 equal-sized sections labeled 1 through 4. In 25 spins, the spinner lands 5 times in section 3. How does this compare to the number of times the pointer is expected to land in section 3?
The pointer lands in section 3 less often than expected.
Ashley collects colored golf balls from a miniature golf course. She will randomly select one ball from her collection of 9 blue, 7 magenta, and 2 purple golf balls.
What is the sample space?
B, B, B, B, B, B, B, B, B, M, M, M, M, M, M, M, P, P
Suppose you flip four coins, and you want to determine the probability of exactly three of these coins flipping a head. If flipping three heads is a favorable compound event, what ratio can be used to determine this probability?
P(compound event) =Number of favorable outcomes/ Total number of possible outcomes
Henry is going to color a spinner with 16 equal-sized sections. Six of the sections will be black, and 10 of the sections will be purple. Is this spinner fair? If so, explain why. If not, explain how to make it a fair spinner.
No, the spinner is not fair because there are more purple sections than black sections. A fair spinner will have 8 black sections and 8 purple sections.
How can the probability of an event help make predictions?
It can tell us what should happen in a given scenario
The best player on a basketball team makes 75% of all free throws. The second-best player makes 65% of all free throws. The third-best player makes 55% of all free throws. Based on their experimental probabilities, estimate the number of free throws each player will make in their next 80 attempts.
Best player: 60 free throws (75/100=x/80)
Second best: 52 free throws (65/100=y/80)
Third best: 44 free throws (55/100=z/80)
Hannah selects a marble randomly from a jar containing 11 green, 5 yellow, and 4 red marbles. Develop a probability model based on theoretical probability.
S = {G, G, G, G, G, G, G, G, G, G, G, Y, Y, Y, Y, Y, R, R, R, R}
P(G) =11/20; P(Y) =1/4; P(R) =1/5
Make a tree diagram that shows the sample space of rolling a cube with faces numbered 1 through 6 and flipping a fair coin. Using this tree diagram, what is the probability of rolling the number 5 and the coin landing heads up?
P(5, H) = 1/12, or 8.3%