Probability Model

Choose an American household at random. What is the expected number of cars for that household?

• 1.75

• 1.84

• 2.00

• 2.50

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household? HINT: A Probability table may be helpful.

• 2.00

• 2.13

• 1.97

• 1.27

A car dealer buys hybrids for $21,000 each and sells them for $24,500 each. Find his expected weekly profit. Hint: Find E(X), then find the profit on each car sold.

• $2,380

• $5,355

• $8,109

• $37,485

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get? Hint: draw a tree diagram to determine the probability of each outcome, you should have 3 events, then set up the probability model.

• $12.50

• $5

• $7.50

• $10

A bag contains colored beads. Ryan selects a bead at random, records the color, and returns the bead to the bag. -After 15 trials, the experimental probability of selecting a red bead is 1/3, a white bead is 2/5, and a blue bead is 4/15. -On the 16th trial, Ryan selects a yellow bead. -On the 17th trial, Ryan selects a blue bead. Determine the true statments.

• There cannot be an orange bead in the bag.

• There must be exactly 1 yellow bead in the bag.

• After 15 trials, Ryan has selected exactly 6 white beads.

• After 16 trials, the experimental probability of selecting a blue bead is 1/4.

• After 17 trials, the experimental probability of selecting a red bead is 5/17.

Sienna has a bag of tiles containing the letters A, B, C, D, and E. She selects a tile at random, records the letter, and then puts the letter back in the bag. Then she repeats the process. The table shows the results of her experiment. If she did the trial 1,000 times, how many times would she expect to pull the letter D?

• 7

• 18

• 175

• 125

Tio has a bag of colored balloons. He selected a balloon at random, records the color, and replaces the balloon in the bag. -After 40 trials, the experimental probability of selecting a red balloon is 1/4, a yellow balloon is 9/20, and a green balloon is 3/10.-On the 41st trial, he selects a red balloon.-On the 42nd trial, he selects a white balloon. Determine the true statements based on the given data.

• There cannot be a purple balloon in the bag.

• There are at least 9 yellow balloons in the bag.

• After 40 trials, Tio has selected 12 green balloon.

• After 41 trials, the probability of selecting a red balloon is 11/41.

• After 42 trials, the probability of selecting a yellow balloon is 9/20.

A bag contains ping-pong balls that are numbered from 1 to 75. Peyton randomly selects a ping-pong ball from the bag, records the number that is on it, and puts it back in the bag. The results of the first 6 trials are: 13, 70, 17, 62, 38, and 64.

Based on the results, how many times is Peyton expected to select an odd-numbered ping-pong ball in the next 30 trials.

• 2/6

• 1/3

• 20

• 10

Janna and Ashley are each given a bag containing cards. A card is selected 30 times. Each card has a picture of either a cat, a dog, a rabbit, or a squirrel. Janna and Ashley each selected a card a random from their bag, record the name of the animal, and replace the card. The results of the experiment are shown in the table. Which prediction is the most reasonable, based on the results of the experiment?

• If Janna selects a card 15 more times, about 4 of them will be dog cards.

• If Janna selects a card 24 more times, about 16 of them will be rabbit cards.

• If Ashley selects a card 48 more times, about 27 of them will be squirrel cards.

• If Ashley selects a card 60 more times, about 45 of them will be cat cards.

A car dealership recorded the vehicle preferences of its customers. The results are shown in the table. Predict each outcome.

• Of the next 40 customers, 5 are expected to prefer a minivan.

• Of the next 50 customers, 9 are expected to prefer an SUV.

• Of the next 30 customers, 15 are expected to prefer a van.

• Of the next 60 customers, 24 are expected to prefer a compact car.