What is the probability of selecting two males given that both are grey?

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In summary, the probability of selecting two males given that both are grey is 1/28. This can be calculated by taking the probability of the first mouse being male (1/4) and the probability of the second mouse being male (1/7) and multiplying them together. This is because, with conditional probability, we only consider the subset of events that meet the given condition.
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So I am having more problems with my homework...

For this problem, assume there are 6 grey females, 2 grey males, 6 white females, and 2 white males. Two mice are randomly selected. What is the probability of selecting two males given that both are grey?

So for selecting two males, I was thinking of 4/12, since there are 4 males in total out of 12. Then for the grey I was thinking of 8/12, since there are 8 grey mice. However, that did not work once I plugged it into the formula...

I thought of using combinations, but I am not sure how that would work and how I should write that. I was thinking of C(4,2)/C(12/2) for the intersection of grey mice and male, and for the "given that both are grey" C(8,2)/C(12,2)...?

Tbh, I am not sure of what I am doing...
 
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So, conditional probability has the effect of "narrowing your world", so to speak. The two mice are both grey, so you can completely ignore the whites.

You pick the first grey mouse without replacement (I think that's understood, though it's good to be clear, because it does change probabilities). What's the probability that it's male? Now pick the second grey mouse, assuming that the first one you picked was male. What's the probability that this second one is male?
 
  • #3
Given that both mice are gray then we can ignore the other mice. There are 6 gray females and 2 gray males for a total of 8 gray mice. The probability the first mouse drawn is male is 2/8= 1/4. There are then 6 gray females and 1 gray male. The probability the second mouse drawn is male is 1/7. Given that the two mice drawn are gray the probability they are male is (1/4)(1/7)= 1/28.
 

FAQ: What is the probability of selecting two males given that both are grey?

1. What does "selecting two males" mean in this scenario?

In this scenario, "selecting two males" means randomly choosing two individuals with the male gender.

2. How is the probability of selecting two males calculated given that both are grey?

The probability of selecting two males given that both are grey can be calculated by dividing the number of grey males by the total number of grey individuals in the population.

3. Is the probability of selecting two males given that both are grey affected by the size of the population?

Yes, the probability of selecting two males given that both are grey can be affected by the size of the population. If the population size is larger, the probability may be lower due to a larger pool of individuals to choose from.

4. How does the probability of selecting two males given that both are grey change if the individuals are not chosen randomly?

If the individuals are not chosen randomly, the probability of selecting two males given that both are grey may be biased and may not accurately reflect the true probability in the population.

5. Can the probability of selecting two males given that both are grey ever be 100%?

It is possible for the probability of selecting two males given that both are grey to be 100% if there are only grey males in the population. However, if there are other genders and colors present, the probability will be less than 100%.

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