A nickel is flipped and a dime is flipped.
1. What is the probability of obtaining exactly one head?
A bag contains five balls numbered 0 through 4. Two balls are chosen at random in succession. The first ball is replaced before the second is chosen.
1. What is the probability that the first ball has an odd number?
2. What is the probability that the second ball has an odd number?
3. What is the probability that both balls have odd numbers?
4. What is the probability that neither ball has an odd number?
To find the answers to these probability questions, we need to first understand how many possible outcomes there are in each scenario.
For the nickel and dime question, there are 2 possible outcomes for each coin flip - either a head or a tail. Since there are two coins being flipped, the total number of possible outcomes is 2 * 2 = 4.
1. To find the probability of obtaining exactly one head, we need to determine how many favorable outcomes there are. In this case, there are two favorable outcomes - either the nickel is a head and the dime is a tail, or the nickel is a tail and the dime is a head. Therefore, the probability is 2/4, which simplifies to 1/2.
For the bag of numbered balls question, there are 5 balls numbered 0 through 4, resulting in a total of 5 possible outcomes when drawing one ball. Since the first ball is replaced before the second is chosen, the number of possible outcomes remains the same for both draws.
1. The probability of the first ball having an odd number can be calculated by finding the number of favorable outcomes (3 balls with odd numbers) divided by the total number of possible outcomes (5 balls). Therefore, the probability is 3/5.
2. Similarly, since the second ball is also chosen from the same set of balls, the number of favorable outcomes (3 balls with odd numbers) remains the same, but now the total number of possible outcomes is reduced to 4 because one ball has already been chosen. Therefore, the probability is 3/4.
3. To find the probability that both balls have odd numbers, we need to multiply the probabilities of the individual events together. The probability of drawing an odd number for the first ball is 3/5, and since the ball is replaced, the probability of drawing an odd number for the second ball is also 3/5. Hence, the probability is (3/5) * (3/5) = 9/25.
4. Finally, to find the probability that neither ball has an odd number, we need to find the probability of both balls having even numbers. There are 2 even-numbered balls (0 and 4) out of the total 5 balls. So the probability of drawing an even number for the first ball is 2/5, and for the second ball, since it's replaced, it remains 2/5. Therefore, the probability is (2/5) * (2/5) = 4/25.