Question 1

Find the Probability of One Event and a Second Event Occurring
-A game spinner has regions that are numbered 1 through 9. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 5?

Accepted Answer

The probability of landing on 3 the first time is $\frac{1}{9}$ since there are 9 numbers. The probability of landing on 5 the second time is also $\frac{1}{9}$. Since these are independent events, multiply the probabilities: $\frac{1}{9} \times \frac{1}{9} = \frac{1}{81}$.

Question 2

Find the Probability of One Event and a Second Event Occurring
-Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?

Accepted Answer

The probability of drawing a 4 from Urn A is $\frac{1}{6}$ since there are 6 balls, and the probability of drawing a 2 from Urn B is $\frac{1}{5}$ since there are 5 balls. Multiplying these probabilities gives $\frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$.

Question 3

Find the Probability of One Event and a Second Event Occurring
-An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. What is the probability that the first and second balls will be a 7?

Accepted Answer

There are 20 options for the first ball and 20 options for the second ball, making a total of 400 possible outcomes. Since we want both balls to be 7, there is only one favorable outcome. Therefore, the probability is 1/400.

Quiz 8: Sequences, Induction, and Probability

Find the Probability of One Event and a Second Event Occurring -A game spinner has regions that are numbered 1 through 9. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 5?

Find the Probability of One Event and a Second Event Occurring -Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?

Find the Probability of One Event and a Second Event Occurring -An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. What is the probability that the first and second balls will be a 7?