ACT Probability and Stats

Front

What is the probability of rolling an even number on a six-sided die?

Back

Tags

CCSS.7.SP.C.7B

Front

Define probability.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Tags

CCSS.7.SP.C.5

Front

What is the formula for calculating the probability of an event?

Back

The probability of an event is calculated as: \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)

Tags

CCSS.7.SP.C.7A

Front

If a jar contains 30% blue, 25% red, and 36 green gumballs, how do you find the total number of gumballs?

Back

Let the total number of gumballs be x. Since 36 green gumballs represent 45% of the total, set up the equation: \( 0.45x = 36 \) to find x.

Tags

CCSS.6.EE.B.7

Front

What is the probability of drawing a 10 or a diamond from a standard deck of 52 cards?

Back

There are 4 tens and 13 diamonds, but one of the tens is a diamond. Thus, the probability is: \( P = \frac{4 + 13 - 1}{52} = \frac{16}{52} = 0.308 \)

Tags

CCSS.HSS.CP.B.7

Front

Explain the concept of independent events in probability.

Back

Independent events are those whose outcomes do not affect each other. For example, rolling a die and flipping a coin are independent events.

Tags

CCSS.HSS.CP.A.5

Front

What is the probability of drawing a face card from a standard deck of cards?

Back

There are 12 face cards (3 in each of the 4 suits), so the probability is: \( P = \frac{12}{52} = \frac{3}{13} \)

Tags

CCSS.7.SP.C.7B

Front

How do you calculate the expected value of a random variable?

Back

The expected value is calculated as: \( E(X) = \sum (x_i \cdot P(x_i)) \) where x_i are the outcomes and P(x_i) are their probabilities.

Tags

CCSS.HSS.MD.A.2

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, selecting 2 out of 3 items: (A, B) is different from (B, A) in permutations but the same in combinations.

Front

If the probability of an event is 0.7, what is the probability of the event not occurring?

Back

The probability of the event not occurring is: \( P(not E) = 1 - P(E) = 1 - 0.7 = 0.3 \)

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4