Mixed Probability

Four people enter their names into a drawing. The winner receives one of two different prizes that are randomly selected. The tree diagram represents all possible outcomes. What is the probability that Ang wins and is given a mug? Write your probability as a decimal.

Stephanie uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Which of the following statements is true? Select all that apply.

• The probability of the pointer landing on an even-numbered section is about 66.67%

• It is impossible that the pointer will land on 1.

• It is less likely that the pointer will land on an odd-numbered section.

• It is certain that the pointer will land on a number less than 6.

• No; the product of the probabilities is less than 1.

• No; the sum of the probabilities is greater than 1.

• Yes; the product of the probabilities is less than 1.

• Yes; the sum of the probabilities is greater than 1.

Shianne plays a game by rolling two number cubes with sides numbered 1 through 6. To win the game, the sum of the numbers facing up must be 11. What is the probability that Shianne will win the game?

What is the experimential probability of spinning a green? (use a reduced fraction)

Mathematical Equivalence

ON

A sports bag contains 3 tennis balls, 4 baseballs, and 8 golf balls. Each is equally likely to be chosen. Which of the following models could be used to simulate this situation?

• flipping a coin fifteen times

• spinning a spinner with three equal sections

• choosing from 3 red marbles, 4 yellow marbles, and 8 blue marbles

• rolling a number cube fifteen times

In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population?

• Let the even digits represent birds with a wingspan greater than 10 inches and the odd digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits 0 and 1 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 2 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

• Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

Vy is shopping for a car. It comes in red, blue, or silver. She can also choose a 2-door and 4-door version along with a manual or automatic transmission. What is the theoretical probability that Vy will pick 4-door car, automatic transmission and it being red or blue?

Mathematical Equivalence

ON

Probability model

• a description of some random process that consists of two parts, the sample space and the probability for each outcome

• any collection of outcomes from some random process

Madeleine spins the pointer of a spinner. The spinner has 7 equal-sized sections labeled 1 to 7. What is the probability that Madeleine will spin a 7?