ACT Prep Probability

Theoretical

100

Maria is flipping a coin and spinning a spinner. The spinner has 4 equal sections labeled A-D. What is the probability the coin will land on heads and the spinner will land on the letter "A"?

1/8 or 0.125, or 12.5%

200

The classic wood carousel at Carousel Park in Hampton, VA has 32 jumping horses and 16 standing horses. What is the probability of randomly selecting a jumping horse?

2/3, 0.6666..., 67%

300

What is the probability of rolling two odd numbers in a row with a standard number cube?

1/4, or 0.25, or 25%

400

There are 3 red marbles, 2 green marbles, and 1 yellow marble in a box. One marble is taken out and not replaces. A second marble is then taken out and not replaced. What is the probability both marbles that were taken out are red?

1/5, or 0.20, or 20%

500

Jarvonya spins a spinner with 5 equal sections numbered 1-5 and she spins another spinner with 5 equal sections with the letters A-E. What is the probability she will spin a 4 and a B?

1/25 or 0.04, or 4%

Experimental

100

Hasaan has a spinner with 5 equal sections, each a different color. After only 10 spins, the pointer had landed on red 40% of the time. After a whopping 1,000 spins, the pointer landed on red only 22% of the time. How can Hasaan account for this change in experimental probability?

As the number of trials increase, the experimental probability reaches closer to the theoretical probability. (The Law of Large Numbers)

200

Pat's Pizza made 21 cheese pizzas, 14 veggie pizzas, 23 pepperoni pizzas, and 14sausage pizzas yesterday.

Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?

17/24, .7083, 71%

300

A letter tile is randomly selected from a bag, recorded, and replaced 100 times. The results are listed below. What is the experimental probability of selecting the letter "E"? A = 16 E = 11 I = 29 O = 19 U = 25

11/100 or 0.11, or 11%

400

Pedro recorded the types of birds that visit his bird feeder. Based on the results below, what is the probability the next bird will be a chickadee? Woodpecker = 3 Chickadee = 5 Cardinal = 1 Sparrow = 13 Blue Jay = 3

1/5, or 0.20, or 20%

500

A six-sided die is thrown 50 times. Using the list below, how does the theoretical probability of rolling a 3 compare to the experimental probability of rolling a 3?  Out of 44 total rolls the dice landed on1  4 times, 8 12times, 2  5times, 6  10times, 3 6 times, and 7  7times 

The theoretical probability is higher than the experimental probability. (Theoretical = 17%, Experimental = 14%)

Counting Principle

100

You are trying to decide what to wear to school. You know you have a green pair of pants, a red pair, and a blue pair. You also have a brown shirt, a plaid shirt, and a yellow shirt. How many different outfit combinations can you make?

9

200

What is the number of possible outcomes for spinning one spinner with 8 equal sections and another spinner with 6 equal sections?

48 possible outcomes

300

Amiya and Keyshawn are candidates for class president of the 7th grade. Ajaye, Chishon, and Laura are candidates for vice president. How many winning combinations are possible?

6

400

Ms. French is packing for a trip. She packs a white blouse, a pink blouse, a blue blouse, and a green blouse. She also packs a black suit, a navy blue suit, and a gray suit. What is the probability that the first outfit she wears is the gray suit with a pink blouse?

1 out of 12

500

What is the probability of rolling three 4's in a row on a number cube?

1/216

How Likely is it?

100

How likely is it that a coin is flipped and lands on tails?

Equally likely

200

How likely is it that a number cube is tossed and lands on 3?

Unlikely

300

How likely is it that a number cube is tossed and it lands on 8?

never going to happen

400

How likely is it that a number cube is tossed and lands on any number 1-6?

Certain

500

How likely is it that a number cube lands on 2 and a coin lands on heads?

unlikely

Compound Events

100

The probability of rain on Monday is 0.1. The probability of rain on Tuesday is 0.. What is the probability of rain on both Monday and Tuesday?

0.08

200

A coin is tossed and a die is rolled. What is the probability that the coin shows tails and the die shows a 3?

1/12, 0.08333, 8.33%

300

Two urns contains green and yellow balls. Urn 1 contains 3 green and 4 yellow balls. Urn 2 contains 5 green and 6 yellow balls. A ball is drawn from each urn. What is the probability that both balls are green?

15/77, 0.195

400

A bag contains 2 yellow marbles and 5 red marbles. Two marbles are drawn at random. One marble is drawn and NOT replace, then a second marble is drawn. What is the probability that the first marble is red and the second one is yellow?

5/21, 0.238

500

A drawer contains 5 red socks, 7 white socks, and 4 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the first sock and the second sock are both red. 

1/12, 0.08333