Independent and 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.

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.

Front

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

Back

To calculate the probability of two independent events A and B occurring together, multiply their individual probabilities: P(A and B) = P(A) * P(B).

Front

How do you calculate the probability of two dependent events occurring together?

Back

To calculate the probability of two dependent events A and B occurring together, use the formula: P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given that A has occurred.

Front

What is the probability of drawing a red marble from a bag containing 3 red, 4 gray, 6 white, and 5 black marbles?

Back

The probability of drawing a red marble is P(Red) = Number of Red Marbles / Total Number of Marbles = 3 / (3 + 4 + 6 + 5) = 3/18 = 1/6.

Front

If a marble is drawn and not replaced, how does it affect the probability of drawing a second marble?

Back

If a marble is drawn and not replaced, the total number of marbles decreases, which affects the probability of drawing a second marble. The new probability is calculated based on the remaining marbles.

Front

What is the probability of drawing a gray marble after drawing a red marble without replacement?

Back

If a red marble is drawn first and not replaced, the probability of drawing a gray marble next is P(Gray) = Number of Gray Marbles / Remaining Total = 4 / (Total - 1).

Front

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

Back

The formula for calculating the probability of an event is P(Event) = Number of favorable outcomes / Total number of possible outcomes.

Front

What is the probability of landing on red or yellow if a spinner has 7 sections, 4 red and 3 yellow?

Back

The probability of landing on red or yellow is P(Red or Yellow) = (Number of Red + Number of Yellow) / Total Sections = (4 + 3) / 7 = 7/10.

Front

In a game of Scrabble, if you need to choose two tiles, how do you calculate the probability of choosing an 'E' and then an 'H'?

Back

The probability of choosing an 'E' first and then an 'H' is calculated as P(E) * P(H|E), where P(H|E) is the probability of choosing 'H' after 'E' has been chosen.