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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
no information about the spinner or the die (or dice?)
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
Sure! I can help you determine the probability of these compound events. To find the probability, we'll need to divide the number of favorable outcomes by the total number of possible outcomes. Let's go through each scenario step by step:
1. Spinning a 4 and rolling a number:
To determine the probability, we need to know the total number of possible outcomes for each event. Let's assume that the spin has numbers 1 through 6, and the roll has numbers 1 through 6 as well.
For spinning a 4 on the spinner, there is only 1 favorable outcome (the number 4) and 6 possible outcomes in total.
For rolling a number, there are 6 possible outcomes (numbers 1 through 6) and 6 favorable outcomes (rolling any number).
So, to find the probability of spinning a 4 and rolling a number, we multiply the probabilities:
P(spinner = 4 AND roll = number) = P(spinner = 4) * P(roll = number)
= (1/6) * (6/6)
= 1/6
Therefore, the probability of spinning a 4 and rolling a number is 1/6.
2. Spinning an even number and rolling a 1 or 2:
Similarly, we need to determine the probabilities for each individual event.
For spinning an even number, there are 3 even numbers out of 6 possible outcomes (2, 4, and 6), so the probability is 3/6 or simplifying it, 1/2.
For rolling a 1 or 2, there are 2 favorable outcomes (numbers 1 and 2) and 6 possible outcomes.
To find the probability of both events occurring, we multiply the probabilities:
P(spinner = even AND roll = 1 or 2) = P(spinner = even) * P(roll = 1 or 2)
= (1/2) * (2/6)
= 1/6
Therefore, the probability of spinning an even number and rolling a 1 or 2 is 1/6.
3. Spinning a 3, 4, or 5 and rolling an odd number:
To find the probability, we'll calculate the probabilities for each event separately.
For spinning a 3, 4, or 5, there are 3 favorable outcomes (the numbers 3, 4, and 5) out of 6 possible outcomes.
So the probability is 3/6 or simplifying it, 1/2.
For rolling an odd number, there are 3 favorable outcomes (numbers 1, 3, and 5) out of 6 total outcomes.
The probability of both events occurring is:
P(spinner = 3, 4, or 5 AND roll = odd number) = P(spinner = 3, 4, or 5) * P(roll = odd number)
= (1/2) * (3/6)
= 1/4
Therefore, the probability of spinning a 3, 4, or 5 and rolling an odd number is 1/4.
4. Spinning an odd number and rolling an even number:
For spinning an odd number, there are 3 favorable outcomes (numbers 1, 3, and 5) out of 6 possible outcomes.
For rolling an even number, there are 3 favorable outcomes (numbers 2, 4, and 6) out of 6 total outcomes.
To find the probability of both events occurring, we multiply the probabilities:
P(spinner = odd number AND roll = even number) = P(spinner = odd number) * P(roll = even number)
= (3/6) * (3/6)
= 9/36
= 1/4
Therefore, the probability of spinning an odd number and rolling an even number is 1/4.
I hope this helps you understand how to calculate the probabilities for compound events. Let me know if you have any further questions!