Understanding Probability Basics

What is the probability of rolling a sum of 7 with two six-sided dice?

Answer explanation

To find the probability of rolling a sum of 7 with two six-sided dice, we count the combinations: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — totaling 6 outcomes. There are 36 possible outcomes, so the probability is \( \frac{6}{36} = \frac{1}{6} \).

If two events A and B are independent, what is the probability of both A and B occurring?

Answer explanation

For independent events A and B, the probability of both occurring is given by the product of their individual probabilities: P(A) × P(B). Thus, the correct answer is P(A) × P(B).

What is the probability of drawing an ace from a standard deck of 52 playing cards?

Answer explanation

A standard deck has 52 cards, including 4 aces. The probability of drawing an ace is the number of favorable outcomes (4) divided by the total outcomes (52), which simplifies to \( \frac{1}{13} \).

Which of the following is a valid probability value?

• 1.5

• -0.2

• 0.75

• 2

Answer explanation

A valid probability value must be between 0 and 1, inclusive. The only choice that meets this criterion is 0.75, as 1.5, -0.2, and 2 are outside the valid range.

If the probability of an event is 0, what does this mean?

• The event is certain to occur.

• The event is impossible.

• The event is equally likely to occur or not occur.

• The event will occur half of the time.

Answer explanation

A probability of 0 indicates that an event cannot occur under any circumstances. Therefore, the correct interpretation is that the event is impossible.

What is the probability of flipping a coin and getting heads?

Answer explanation

The probability of flipping a fair coin and getting heads is 1 out of 2 possible outcomes (heads or tails). Therefore, the correct answer is \(\frac{1}{2}\).

If the probability of an event A is 0.3, what is the probability of the complement of A?

• 0.3

• 0.7

• 1.0

• 0.5

Answer explanation

The probability of the complement of event A, denoted as A', is calculated as 1 minus the probability of A. Since P(A) = 0.3, P(A') = 1 - 0.3 = 0.7. Therefore, the correct answer is 0.7.

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

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: \( \frac{26}{52} = \frac{1}{2} \).

If two events A and B are mutually exclusive, what is the probability of either A or B occurring?

Answer explanation

For mutually exclusive events A and B, the probability of either A or B occurring is the sum of their individual probabilities. Thus, the correct formula is P(A) + P(B).

What is the probability of rolling a 3 on a six-sided die?

Answer explanation

A six-sided die has 6 faces, each showing a different number from 1 to 6. The probability of rolling any specific number, including 3, is the number of favorable outcomes (1) divided by the total outcomes (6), which is \(\frac{1}{6}\).