1. A jar contains 5 red marbles and 3 green marbles. What is the probability of selecting a red marble and then selecting another red marble without replacement?
Solution: The probability of selecting a red marble from the jar on the first pick is 5/8. After one red marble has been selected and removed from the jar, there are now 4 red marbles and 3 green marbles left in the jar. Therefore, the probability of selecting another red marble on the second pick is 4/7. To find the probability of both events occurring, we multiply the probabilities together: 5/8 x 4/7 = 5/14
2. A bag contains 6 blue marbles, 4 red marbles, and 2 green marbles. What is the probability of selecting a blue marble and then selecting a red marble without replacement?
Solution: The probability of selecting a blue marble from the bag on the first pick is 6/12, which can be simplified to 1/2. After one blue marble has been selected and removed from the bag, there are now 4 red marbles and 11 total marbles left in the bag. Therefore, the probability of selecting a red marble on the second pick is 4/11. To find the probability of both events occurring, we multiply the probabilities together: 1/2 x 4/11 = 2/11
3. A coin is flipped twice. What is the probability of getting heads on the first flip and tails on the second flip?
Solution: The probability of getting heads on the first flip is 1/2, and the probability of getting tails on the second flip is also 1/2. To calculate the probability of both events occurring, we multiply the probabilities together: 1/2 x 1/2 = 1/4
4. A deck of cards contains 52 cards, including 12 face cards (4 kings, 4 queens, and 4 jacks). If a card is randomly selected from the deck and then placed back in the deck, and then another card is randomly selected, what is the probability of selecting a king on the first pick and a queen on the second pick?
Solution: The probability of selecting a king on the first pick is 4/52, which can be simplified to 1/13. After the first card has been selected and replaced in the deck, there are still 4 kings and now 51 total cards in the deck. Therefore, the probability of selecting a queen on the second pick is 4/51. To find the probability of both events occurring, we multiply the probabilities together: 1/13 x 4/51 = 4/663
Independent and dependent events practice
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