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determine the probability of each compound event described.Show work.
1. spinning a 4 and rolling a
2.spinning an even number and rolling a 1 or2
3.spinning a 3, 4, or 5 and rolling an odd number
4.spinning an odd number and rolling an even number
still incomplete.
get a grip, willya?
1. spinning a 3 and rolling a 3
2. spinning an odd number and rolling a 5 or 6
3. spinning an even number and rolling an odd number
4. spinning an even number and rolling an odd number
5. spinning a 3 or 7 and rolling an odd number
To determine the probability of each compound event, we need to know the total number of favorable outcomes and the total number of possible outcomes.
1. Spinning a 4 and rolling a _.
Assuming that the blank is indicating rolling any number from 1 to 6, we can calculate the probability as follows:
Spinning a 4: There is 1 favorable outcome (the number 4), and there are 6 possible outcomes (numbers 1 to 6 on the die). So, the probability is 1/6.
Rolling any number: There are 6 favorable outcomes (numbers 1 to 6), and there are 6 possible outcomes. So, the probability is 6/6 = 1.
To find the probability of both events happening, we multiply the probabilities together:
Probability = (1/6) * 1 = 1/6
2. Spinning an even number and rolling a 1 or 2.
Spinning an even number: There are 3 favorable outcomes (2, 4, and 6), and there are 6 possible outcomes. So, the probability is 3/6 = 1/2.
Rolling a 1 or 2: There are 2 favorable outcomes (1 and 2), and there are 6 possible outcomes. So, the probability is 2/6 = 1/3.
To find the probability of both events happening, we multiply the probabilities together:
Probability = (1/2) * (1/3) = 1/6
3. Spinning a 3, 4, or 5 and rolling an odd number.
Spinning a 3, 4, or 5: There are 3 favorable outcomes (3, 4, and 5), and there are 6 possible outcomes. So, the probability is 3/6 = 1/2.
Rolling an odd number: There are 3 favorable outcomes (1, 3, and 5), and there are 6 possible outcomes. So, the probability is 3/6 = 1/2.
To find the probability of both events happening, we multiply the probabilities together:
Probability = (1/2) * (1/2) = 1/4
4. Spinning an odd number and rolling an even number.
Spinning an odd number: There are 3 favorable outcomes (1, 3, and 5), and there are 6 possible outcomes. So, the probability is 3/6 = 1/2.
Rolling an even number: There are 3 favorable outcomes (2, 4, and 6), and there are 6 possible outcomes. So, the probability is 3/6 = 1/2.
To find the probability of both events happening, we multiply the probabilities together:
Probability = (1/2) * (1/2) = 1/4
Therefore, the probabilities are as follows:
1. Probability of spinning a 4 and rolling any number: 1/6
2. Probability of spinning an even number and rolling a 1 or 2: 1/6
3. Probability of spinning a 3, 4, or 5 and rolling an odd number: 1/4
4. Probability of spinning an odd number and rolling an even number: 1/4
To determine the probability of each compound event, we need to break down the problem into individual events and find the probability of each event separately. Then, we can multiply the probabilities of the individual events together to calculate the probability of the compound event.
Before we proceed to answer the specific questions, let's define the sample spaces for each event:
1. Spinning a 4: The sample space for this event is {1, 2, 3, 4, 5, 6}, as the spinner can land on any number from 1 to 6.
2. Rolling a 1 or 2: The sample space for this event is {1, 2, 3, 4, 5, 6}, as there are six possible outcomes on a fair 6-sided die.
3. Spinning an even number: The sample space for this event is {1, 2, 3, 4, 5, 6}.
4. Rolling a 1 or 2: The sample space for this event is {1, 2, 3, 4, 5, 6}.
Now, let's calculate the probabilities for each compound event:
1. To find the probability of spinning a 4 and rolling "a," we need to multiply the probabilities of spinning a 4 and rolling "a" together. Since "a" is not specified, we cannot provide an exact answer. However, the process to calculate the probability of any given number "a" would be as follows:
a. Determine the probability of spinning a 4: In this case, since there is only one favorable outcome (spinning a 4) and six possible outcomes (numbers 1 to 6), the probability of spinning a 4 is 1/6.
b. Determine the probability of rolling "a" (where "a" can be any number from 1 to 6): Since "a" is not specified, we cannot provide an exact answer without further information.
2. To find the probability of spinning an even number and rolling a 1 or 2, we need to multiply the probabilities of spinning an even number and rolling a 1 or 2 together.
a. Determine the probability of spinning an even number: There are three even numbers on the spinner (2, 4, and 6). So, the probability of spinning an even number is 3/6, or simplifying, 1/2.
b. Determine the probability of rolling a 1 or 2: There are two favorable outcomes (1 and 2) and six possible outcomes (numbers 1 to 6). Therefore, the probability of rolling a 1 or 2 is 2/6, which simplifies to 1/3.
Now, multiply the probabilities: (1/2) * (1/3) = 1/6.
So, the probability of spinning an even number and rolling a 1 or 2 is 1/6.
3. To find the probability of spinning a 3, 4, or 5 and rolling an odd number, we need to multiply the probabilities of spinning 3, 4, or 5 and rolling an odd number together.
a. Determine the probability of spinning a 3, 4, or 5: There are three favorable outcomes (3, 4, and 5) and six possible outcomes (numbers 1 to 6). Therefore, the probability of spinning a 3, 4, or 5 is 3/6, or simplifying, 1/2.
b. Determine the probability of rolling an odd number: There are three odd numbers on the die (1, 3, and 5). So, the probability of rolling an odd number is 3/6, or simplifying, 1/2.
Now, multiply the probabilities: (1/2) * (1/2) = 1/4.
So, the probability of spinning a 3, 4, or 5 and rolling an odd number is 1/4.
4. To find the probability of spinning an odd number and rolling an even number, we need to multiply the probabilities of spinning an odd number and rolling an even number together.
a. Determine the probability of spinning an odd number: There are three odd numbers on the spinner (1, 3, and 5). So, the probability of spinning an odd number is 3/6, or simplifying, 1/2.
b. Determine the probability of rolling an even number: There are three even numbers on the die (2, 4, and 6). So, the probability of rolling an even number is 3/6, or simplifying, 1/2.
Now, multiply the probabilities: (1/2) * (1/2) = 1/4.
So, the probability of spinning an odd number and rolling an even number is 1/4.