What is the definition of probability?

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

If a coin is flipped, what is the probability of getting heads?

The probability of getting heads when flipping a fair coin is 1/2, since there are two possible outcomes (heads or tails) and both are equally likely.

In a standard deck of 52 playing cards, what is the probability of drawing an Ace?

There are 4 Aces in a standard deck of 52 cards. Therefore, the probability of drawing an Ace is 4/52, which simplifies to 1/13.

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

To find the probability, we first count the outcomes that yield a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), which totals 6 outcomes. There are 36 possible outcomes when rolling two dice. Thus, the probability is 6/36, which simplifies to 1/6.

If the probability of event A occurring is 0.3, what is the probability of event A not occurring?

The probability of event A not occurring is calculated as 1 minus the probability of A occurring. Therefore, the probability of A not occurring is 1 - 0.3 = 0.7.

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

The probability of an event E occurring is given by P(E) = Number of favorable outcomes / Total number of outcomes.

What is the probability of selecting a red ball from a bag containing 3 red and 2 blue balls?

There are 3 favorable outcomes (red balls) out of 5 total balls. Thus, the probability is P(red) = 3/5.

What is the probability of not rolling a 1 on a fair six-sided die?

The probability of rolling a 1 is 1/6. Therefore, the probability of not rolling a 1 is 1 - 1/6 = 5/6.

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

The sample space for flipping two coins is {HH, HT, TH, TT}. The outcomes with at least one head are HH, HT, and TH, giving 3 favorable outcomes. Thus, P(at least one head) = 3/4.

What is conditional probability?

Conditional probability is the probability of an event A occurring given that event B has occurred, expressed as P(A|B) = P(A and B) / P(B).

Find the probability of drawing a face card from a standard deck of 52 cards.

There are 12 face cards in a standard deck (3 per suit). Therefore, the probability of drawing a face card is P(face card) = 12/52, which simplifies to 3/13.

If a bag contains 5 green, 3 yellow, and 2 red marbles, what is the probability of drawing a yellow marble?

The total number of marbles is 10. The probability of drawing a yellow marble is P(yellow) = 3/10.

What is the probability of rolling a sum greater than 8 with two six-sided dice?

The outcomes that give a sum greater than 8 are: (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6). There are 10 favorable outcomes. Thus, P(sum > 8) = 10/36, which simplifies to 5/18.

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

There are 13 hearts in a standard deck of 52 cards. Therefore, the probability of drawing a heart is P(heart) = 13/52, which simplifies to 1/4.

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

The complement of rolling a 3 is rolling any number except 3. The probability of rolling a 3 is 1/6, so the probability of the complement is P(not 3) = 1 - 1/6 = 5/6.