suppose a single die is rolled find:
a) P(6, given that an odd number is rolled)
b) P(5, given that ann odd number is rolled)
is a) 0 and b) 1/6
A is right.
If you are only considering rolling odd numbers, you might want to consider changing the answer to B. With the available numbers 1-6, there are only 3 odd numbers.
I hope this helps. Thanks for asking.
To find the probabilities, we need to first determine the sample space and then the favorable outcomes.
The sample space for rolling a single die is {1, 2, 3, 4, 5, 6}.
a) P(6, given that an odd number is rolled):
The favorable outcomes in this case are only {1, 3, 5} because these are the odd numbers. And the only favorable outcome that has a 6 is 6 itself. Therefore, the probability P(6, given that an odd number is rolled) is 1 out of 3 or 1/3.
b) P(5, given that an odd number is rolled):
Again, the favorable outcomes are {1, 3, 5}. The only favorable outcome that has a 5 is 5 itself. Therefore, the probability P(5, given that an odd number is rolled) is 1 out of 3 or 1/3.
So, the correct answer is a) P(6, given that an odd number is rolled) is 1/3, and b) P(5, given that an odd number is rolled) is 1/3.
To find the probabilities, we need to understand the sample space and the favorable outcomes in each scenario.
The sample space for rolling a single die is {1, 2, 3, 4, 5, 6}, as there are six possible outcomes.
a) P(6, given that an odd number is rolled)
To find this probability, we need to consider the favorable outcomes when an odd number is rolled. In this case, the favorable outcomes are {1, 3, 5}, as these are the odd numbers on a die.
The probability can be calculated as the number of favorable outcomes divided by the total number of possible outcomes:
P(6, given that an odd number is rolled) = P(6|odd) = Favorable outcomes / Total outcomes
Since the number 6 is not an odd number, there are no favorable outcomes for rolling a 6 given that an odd number is rolled. Therefore, the probability P(6, given that an odd number is rolled) is 0.
b) P(5, given that an odd number is rolled)
Similar to the previous case, the favorable outcomes when an odd number is rolled are {1, 3, 5}.
The probability can be calculated as:
P(5, given that an odd number is rolled) = P(5|odd) = Favorable outcomes / Total outcomes
In this case, there is one favorable outcome (rolling a 5) out of the three possible odd numbers. Therefore, the probability P(5, given that an odd number is rolled) is 1/3, or approximately 0.3333.
To summarize:
a) P(6, given that an odd number is rolled) = 0
b) P(5, given that an odd number is rolled) = 1/3 or approximately 0.3333