# In a certain region, 46% of the population is female.It is known that 5% of males and 2% of females are left-handed.A person is chosen at random and found to be left-handed.What is the probability that this person is a male?

from the region is a Female, Male, and, Left handed, resp.

From what is given, we have,

By Definition,

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To find the probability that a left-handed person chosen at random is a male, we can use Bayes' theorem.

Let ( M ) be the event that the person is male, and ( L ) be the event that the person is left-handed.

Given:

- Probability of being male (( P(M) )) = 54% = 0.54
- Probability of being female (( P(F) )) = 46% = 0.46
- Probability of being left-handed given male (( P(L|M) )) = 5% = 0.05
- Probability of being left-handed given female (( P(L|F) )) = 2% = 0.02

We want to find ( P(M|L) ), the probability that the person is male given that they are left-handed.

Using Bayes' theorem:

[ P(M|L) = \frac{P(L|M) \times P(M)}{P(L)} ]

We can find ( P(L) ) using the law of total probability:

[ P(L) = P(L|M) \times P(M) + P(L|F) \times P(F) ]

Substitute the given values:

[ P(L) = 0.05 \times 0.54 + 0.02 \times 0.46 ]

[ P(L) = 0.027 + 0.0092 ]

[ P(L) = 0.0362 ]

Now, substitute the values into Bayes' theorem:

[ P(M|L) = \frac{0.05 \times 0.54}{0.0362} ]

[ P(M|L) = \frac{0.027}{0.0362} ]

[ P(M|L) \approx 0.7459 ]

Therefore, the probability that a left-handed person chosen at random is male is approximately ( 0.7459 ), or ( 74.59% ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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