In a random experiment of rolling a die, what is the probability of rolling an even number?

The probability P(even number) = 3/6 = 1/2, since the favorable outcomes are 2, 4, and 6.

The probability of drawing a specific red ball from a bag containing 1 black, 1 red, and 1 green ball is ___?

The probability P(red ball) = 1/3, as there is 1 favorable outcome (red ball) out of 3 total outcomes.

If the probability of an event E is 1/4, what is the probability of its complementary event E̅?

The probability P(E̅) = 1 - P(E) = 1 - 1/4 = 3/4.

True or False: An impossible event has a probability of 1.

False. An impossible event has a probability of 0.

What is the sample space when tossing two coins?

The sample space S = {(H,H), (H,T), (T,H), (T,T)} which has 4 possible outcomes.

Fill in the blank: The probability of getting a head when tossing a coin is ___?

1/2, as there are 2 outcomes (head and tail) and 1 favorable outcome (head).

If a die is rolled, what is the probability of not rolling a 5?

The probability P(not 5) = 5/6, since there are 5 favorable outcomes (1, 2, 3, 4, 6) out of 6 total outcomes.

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

The probability P(face card) = 12/52 = 3/13, as there are 12 face cards (kings, queens, jacks).

In an experiment with 10 trials where an event occurs 3 times, what is the empirical probability of the event?

The empirical probability P(event) = 3/10.

True or False: If all outcomes in an experiment are equally likely, then the probability of a specific outcome is always greater than 0.

True, as each outcome must have a non-zero probability.

Calculate the total number of outcomes when rolling three dice.

The total number of outcomes = 6³ = 216.

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

The probability P(not occurring) = 1 - 0.7 = 0.3.

Fill in the blank: The classical probability of winning a game where you have 2 favorable outcomes out of 5 total outcomes is ___?

2/5.

What is the probability of rolling a number less than 3 on a standard die?

The probability P(less than 3) = 2/6 = 1/3, with favorable outcomes being 1 and 2.

If a card is drawn from a standard deck, what is the probability of it being a heart?

The probability P(heart) = 13/52 = 1/4, since there are 13 hearts in the deck.