Probability of Events

What is the probability of rolling a 4 on a standard six-sided die?

• 1/6

• 1/4

• 1/3

• 1/2

Answer explanation

A standard six-sided die has six faces, each showing a different number from 1 to 6. The probability of rolling any specific number, including a 4, is 1 out of 6 possible outcomes, hence the probability is 1/6.

If you flip two coins, what is the probability of getting two heads?

• 1/4

• 1/3

• 1/2

• 2/3

Answer explanation

When flipping two coins, the possible outcomes are HH, HT, TH, TT. Only one outcome (HH) results in two heads. Thus, the probability is 1 favorable outcome out of 4 total outcomes, which is 1/4.

A jar contains 5 red, 8 blue, and 7 green marbles. What is the probability of randomly selecting a blue marble?

• 1/5

• 1/4

• 1/3

• 8/20

Answer explanation

To find the probability of selecting a blue marble, divide the number of blue marbles (8) by the total number of marbles (5 red + 8 blue + 7 green = 20). Thus, the probability is 8/20, which simplifies to 2/5, not 1/3. The correct answer is 8/20.

In a standard deck of 52 cards, what is the probability of drawing a heart or a spade?

• 1/2

• 1/4

• 1/3

• 1/16

Answer explanation

A standard deck has 52 cards, with 13 hearts and 13 spades. The probability of drawing a heart or a spade is (13 + 13) / 52 = 26 / 52 = 1/2. Thus, the correct answer is 1/2.

What is the probability of drawing a red card from a standard deck of 52 cards?

• 1/16

• 1/3

• 1/4

• 1/2

Answer explanation

A standard deck has 52 cards, with 26 red cards (hearts and diamonds). The probability of drawing a red card is the number of red cards divided by the total number of cards: 26/52 = 1/2.

Two dice are rolled. What is the probability that the sum of the numbers is 7?

• 1/3

• 1/12

• 1/6

• 1/36

Answer explanation

When rolling two dice, there are 36 possible outcomes. The pairs that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), totaling 6 outcomes. Thus, the probability is 6/36, which simplifies to 1/6.

Suppose you draw a card from a standard deck. What is the probability of drawing a face card (Jack, Queen, or King)?

• 1/3

• 1/2

• 2/5

• 3/13

Answer explanation

A standard deck has 52 cards, with 12 face cards (3 per suit). The probability of drawing a face card is 12/52, which simplifies to 3/13. Thus, the correct answer is 3/13.

What is the probability of rolling an even number on a standard die?

• 1/6

• 1/2

• 1/4

• 1/3

Answer explanation

A standard die has 6 faces numbered 1 to 6. The even numbers are 2, 4, and 6, totaling 3 even outcomes. Therefore, the probability of rolling an even number is 3 out of 6, which simplifies to 1/2.

If a number us chosen randomly from 1-10, what is the probability that it is a prime number?

• 1/2

• 3/10

• 2/5

• 4/10

Answer explanation

The prime numbers between 1 and 10 are 2, 3, 5, and 7, totaling 4 prime numbers. Since there are 10 possible numbers, the probability is 4/10, which simplifies to 2/5.

Choosing from 8 car models, 5 exterior paint colors and 2 interior colors, what is the total number of outcomes?

• 15

• 40

• 21

• 80

Answer explanation

To find the total outcomes, multiply the number of choices: 8 car models x 5 paint colors x 2 interior colors = 80. Thus, the correct answer is 80.