1. Which of the following is an example of a dependent event?
2. Which of the following is an example of an intendent event?
3. The number cube shown is rolled and the spinner shown is spun. Find P (5 and blue).
4. The number cube shown is rolled and the spinner shown is spun. Find p (and odd number and yellow).
5. There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. Find p (green, then yellow).
1. Drawing a red card from a deck of cards, then drawing another red card without replacing the first one.
2. Rolling a number cube and flipping a coin at the same time.
3. P (5) = 1/6 and P (blue) = 2/5. Since these are independent events, we can multiply their probabilities together to get: P (5 and blue) = P (5) x P (blue) = 1/6 x 2/5 = 1/15.
4. P (odd number) = 3/6 = 1/2 and P (yellow) = 1/5. Since these are independent events, we can multiply their probabilities together to get: P (odd number and yellow) = P (odd number) x P (yellow) = 1/2 x 1/5 = 1/10.
5. P (green) = 5/30, or 1/6. Then, since we did not replace the green gum ball, P (yellow) = 8/29. Since these are dependent events, we can multiply their probabilities together to get: P (green, then yellow) = P (green) x P (yellow|green) = 1/6 x 8/29 = 8/174, or approximately 0.046.
The answer to the question:
1. Which of the following is an example of a dependent event?
A. Flipping two coins
B. Rolling a number cube and spinning a spinner
C. Choosing a card from a deck, replacing it, then choosing another card
D. Choosing a cookie at random, eating it, and then choosing another at random.
2. Which of the following is an example of an intendent event?
A. Choosing one sock at random from your drawer, putting it on, and then choosing another at random.
B. Flipping a coin and rolling a number cube
C. Choosing students at random for basketball teams
D. Removing a marble from a bag, and then choosing without replacing the first.
3. The number cube shown is rolled and the spinner shown is spun. Find P (5 and blue).
A. 4/6
B. 1/24
C. 1/16
D. 1/9
4. The number cube shown is rolled and the spinner shown is spun. Find p (and odd number and yellow).
A. 1/4
B. 3/4
C.3/5
D. 3/20
5. There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. Find p (green, then yellow).
A. 40/900
B. 5/30
C. 8/30
D. 40/870
1. C. Choosing a card from a deck, replacing it, then choosing another card (dependent because the probability of choosing the second card is affected by the choice of the first card)
2. A. Choosing one sock at random from your drawer, putting it on, and then choosing another at random (independent because the choice of the first sock does not affect the probability of choosing the second sock)
3. C. 1/16
4. D. 3/20
5. A. 40/900
1. An example of a dependent event is when the outcome of one event affects the outcome of another event. One example could be drawing two cards without replacement from a deck of cards.
2. It seems like you might have meant to ask for an example of an independent event. An independent event is when the outcome of one event does not affect the outcome of another event. One example could be flipping a coin and rolling a number cube.
3. To find the probability of rolling a 5 and spinning blue, we need to know the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes. If the number cube has six sides and the spinner has four colors, then the total number of outcomes is 6 (sides of the number cube) multiplied by 4 (colors of the spinner) - totaling 24 outcomes. If only one outcome satisfies both conditions (for example, rolling a 5 and spinning blue), then the probability is 1/24.
4. Similarly, to find the probability of rolling an odd number and spinning yellow, we need to know the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes. For example, if the number cube has six sides (with odd numbers being 1, 3, and 5) and the spinner has three colors, then the total number of outcomes is 3 (odd numbers on the number cube) multiplied by 3 (colors of the spinner) - totaling 9 outcomes. If only one outcome satisfies both conditions, then the probability is 1/9.
5. To find the probability of selecting a green gum ball and then selecting a yellow gum ball, we need to know the total number of gum balls and the number of green and yellow gum balls. In this case, there are 9 green gum balls and 8 yellow gum balls. The total number of gum balls is 9 + 5 + 8 + 8 = 30. When selecting the first gum ball, there are 30 possible outcomes. After selecting a green gum ball, there are 29 gum balls remaining, with 8 of them being yellow. Therefore, the probability of selecting a green gum ball, followed by a yellow gum ball is (9/30) * (8/29), simplified to 4/43.