What is the definition of probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 will not occur, while an event with a probability of 1 will certainly occur.

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

The probability of an event A can be calculated using the formula: P(A) = Number of favorable outcomes / Total number of possible outcomes.

If a fair six-sided die is rolled, what is the probability of rolling a number greater than 4?

There are 2 favorable outcomes (5 and 6) out of 6 possible outcomes. Therefore, P(rolling a number greater than 4) = 2/6 = 1/3.

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

There are 13 hearts in a deck of 52 cards. Hence, the probability of drawing a heart is P(Heart) = 13/52 = 1/4.

If two coins are flipped, what is the probability of getting at least one head?

The possible outcomes when flipping two coins are: HH, HT, TH, TT. Out of these 4 outcomes, 3 include at least one head (HH, HT, TH). Thus, P(at least one head) = 3/4.

What is the complement rule in probability?

The complement rule states that the probability of an event A not occurring is equal to 1 minus the probability of A: P(not A) = 1 - P(A).

What is the formula for calculating the probability of independent events A and B occurring together?

For independent events, the probability of both events A and B occurring is given by: P(A and B) = P(A) * P(B).

What is a key strategy for solving probability problems involving 'at least' scenarios?

A common strategy is to use the complement rule: instead of calculating the probability of the event directly, calculate the probability of the event not occurring and subtract it from 1.

In a bag with 3 red, 2 blue, and 5 green marbles, what is the probability of drawing a blue marble?

There are 2 blue marbles out of a total of 10 marbles. Therefore, P(blue marble) = 2/10 = 1/5.

If a card is drawn from a standard deck, what is the probability of drawing a face card?

There are 12 face cards (3 face cards in each of the 4 suits) in a deck of 52 cards. Thus, P(face card) = 12/52 = 3/13.

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

The possible combinations to roll a sum of 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) - totaling 6 favorable outcomes. Since there are 36 total outcomes when rolling two dice, P(sum of 7) = 6/36 = 1/6.