Probability of Independent Events

Front

What is the probability of independent events?

Back

The probability of independent events is the product of their individual probabilities. If two events A and B are independent, then P(A and B) = P(A) * P(B).

Front

Define independent events in probability.

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other(s).

Front

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

Back

P(red) = Number of red marbles / Total number of marbles = 5 / (5 + 3) = 5/8.

Front

What is the formula to calculate the probability of two independent events occurring together?

Back

P(A and B) = P(A) * P(B).

Front

If the probability of spinning a red on a spinner is 1/4 and picking a red marble is 1/2, what is the probability of both occurring?

Back

P(red on spinner and red marble) = P(red on spinner) * P(red marble) = (1/4) * (1/2) = 1/8.

Front

What is the probability of not drawing a blue marble from a bag containing 8 blue, 7 green, and 5 yellow marbles?

Back

P(not blue) = (Number of non-blue marbles) / (Total number of marbles) = (7 + 5) / (8 + 7 + 5) = 12/20 = 3/5.

Front

How do you calculate the probability of drawing a marble, replacing it, and drawing again?

Back

The probability remains the same for each draw since the marble is replaced. Use P(A) * P(B) for independent events.

Front

What is the probability of drawing a yellow marble and then a blue marble from a bag with 8 blue, 7 green, and 5 yellow marbles?

Back

P(yellow, blue) = P(yellow) * P(blue) = (5/20) * (8/20) = 1/10.

Front

If you have a spinner with 4 equal sections (1 red, 1 blue, 1 green, 1 yellow), what is the probability of spinning red?

Back

P(red) = 1/4.

Front

What is the probability of selecting the letter A from the word MATHEMATICIANS?

Back

There are 3 A's in 14 letters, so P(A) = 3/14.