Topic 12: Probability of Independent and Dependent Events

Front

What is the probability of rolling an even number on a 6-sided number cube?

Back

The even numbers on a 6-sided cube are 2, 4, and 6. Therefore, the probability is \( \frac{3}{6} = \frac{1}{2} \).

Front

What is the probability of rolling an even number three times in a row on a 6-sided number cube?

Back

The probability of rolling an even number is \( \frac{1}{2} \). Therefore, the probability of rolling an even number three times in a row is \( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \).

Front

What is the probability of drawing a yellow gummy bear followed by a red gummy bear from a bag containing 4 red, 5 green, and 3 yellow bears without replacement?

Back

The probability of drawing a yellow bear first is \( \frac{3}{12} \) and then a red bear is \( \frac{4}{11} \). Therefore, the combined probability is \( \frac{3}{12} \times \frac{4}{11} = \frac{1}{11} \).

Front

Is the event of spinning a spinner twice and landing on red first and then blue independent or dependent?

Back

This event is independent because the outcome of the first spin does not affect the outcome of the second spin.

Front

What is the probability of drawing two blue marbles from a jar containing 5 red, 3 blue, and 2 green marbles without replacement?

Back

The probability of drawing the first blue marble is \( \frac{3}{10} \) and the second blue marble is \( \frac{2}{9} \). Therefore, the combined probability is \( \frac{3}{10} \times \frac{2}{9} = \frac{1}{15} \).

Front

What is the probability of rolling a number greater than 4 on a number cube and tossing tails on a coin?

Back

The probability of rolling a number greater than 4 (5 or 6) is \( \frac{2}{6} = \frac{1}{3} \) and the probability of tossing tails is \( \frac{1}{2} \). Therefore, the combined probability is \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \).

Front

Define independent events in probability.

Back

Independent events are events where the occurrence of one event does not affect the occurrence of another event.

Front

Define dependent events in probability.

Back

Dependent events are events where the occurrence of one event affects the occurrence of another event.

Front

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

Back

For independent events A and B, the probability is given by \( P(A \text{ and } B) = P(A) \times P(B) \).

Front

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

Back

For dependent events A and B, the probability is given by \( P(A \text{ and } B) = P(A) \times P(B|A) \), where \( P(B|A) \) is the probability of B given A has occurred.