Basic, Independent, Dependent Probability

Front

What is the definition of independent probability?

Back

Independent probability refers to the likelihood of an event occurring that is not affected by the occurrence of another event. For example, flipping a coin and rolling a die are independent events.

Front

What is the definition of dependent probability?

Back

Dependent probability refers to the likelihood of an event occurring that is affected by the occurrence of another event. For example, drawing cards from a deck without replacement is a dependent event.

Front

What is the formula for calculating the probability of independent events?

Back

P(A and B) = P(A) * P(B), where A and B are independent events.

Front

What is the formula for calculating the probability of dependent events?

Back

P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given that A has occurred.

Front

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

Back

P(red) = 3/5.

Front

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

Back

P(blue) = 2/5.

Front

What is the probability of drawing two red marbles in succession without replacement from a bag containing 3 red marbles?

Back

P(Red1) = 3/5, P(Red2|Red1) = 2/4, so P(Red1 and Red2) = (3/5) * (2/4) = 3/10.

Front

What is the probability of drawing a pink Starburst followed by a yellow Starburst from a pack containing 3 orange, 6 pink, 1 yellow, and 5 red Starbursts?

Back

P(pink then yellow) = (6/15) * (1/14) = 6/210 = 1/35.

Front

What is the probability of choosing a vowel from the letters in 'MATHEMATICIANS'?

Back

There are 6 vowels (A, E, I) in 14 letters, so P(vowel) = 6/14 = 3/7.

Front

What is the probability of choosing the letter M, and then the letter A from 'MATHEMATICIANS'?

Back

P(M) = 2/14, P(A|M) = 3/14, so P(M and A) = (2/14) * (3/14) = 6/196 = 3/98.