Front

What is the definition of probability?

Back

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.

Front

How do you calculate the probability of a single event?

Back

The probability of a single event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Front

What is the formula for calculating the probability of choosing a specific color from a set of colored items?

Back

P(color) = (Number of items of that color) / (Total number of items).

Front

What is the probability of choosing a vowel from the word 'MATHEMATICS'?

Back

The probability is calculated by counting the vowels (A, E, A, I) and dividing by the total letters (11), resulting in 4/11.

Front

How do you determine the total number of combinations when selecting multiple items?

Back

Use the formula: Total combinations = (Number of choices for item 1) * (Number of choices for item 2) * ... * (Number of choices for item n).

Front

What is the probability of selecting two dimes in succession without replacement?

Back

P(both dimes) = (Number of dimes/Total coins) * (Number of dimes left/Total coins left) = (18/40) * (17/39) = 51/260.

Front

What is the difference between probability with replacement and without replacement?

Back

With replacement means the item is returned to the set before the next selection, while without replacement means the item is not returned, affecting the total number of outcomes.

Front

How do you calculate the probability of two independent events occurring?

Back

For independent events, multiply the probabilities of each event: P(A and B) = P(A) * P(B).

Front

What is the probability of selecting a green marble first and a yellow marble second with replacement?

Back

P(green first) * P(yellow second) = (2/11) * (3/11) = 6/121.

Front

What is a favorable outcome in probability?

Back

A favorable outcome is an outcome that satisfies the conditions of the event whose probability is being calculated.