in a sample of 1000 people <525 men and 475 women>,113 are left handed<63 men and 50 women>.the results of the sample are shown in the table.find the probability that a randomly selected person is a left handed,given that she is a woman.<round to 3 decimal places
It would help if you proofread your questions before you posted them.
"<" means "is less than" and ">" means "is more than."
Did you mean to use parentheses ()?
Does the table give you more information?
50 left-handed women/475 total women = ?
yes
To find the probability that a randomly selected person is left-handed, given that they are a woman, you need to use conditional probability.
The conditional probability formula is: P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of event A occurring given that event B has occurred, P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
In this case, event A is being left-handed, and event B is being a woman.
From the table, we see that there are 475 women and 50 left-handed women.
P(A ∩ B) = 50 (probability of being left-handed and a woman)
P(B) = 475 (probability of being a woman)
Plugging these values into the formula:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = 50 / 475
Now we can calculate the probability:
P(A|B) = 0.105
Therefore, the probability that a randomly selected person is left-handed, given that they are a woman, is approximately 0.105 (rounded to 3 decimal places).
To find the probability that a randomly selected person is a left-handed, given that she is a woman, you need to use conditional probability.
First, you need to determine the number of women in the sample. In this case, there are 475 women out of 1000 people.
Next, you need to determine the number of women who are left-handed. According to the given data, there are 50 women who are left-handed.
Now, you can use the formula for conditional probability:
Probability = Number of favorable outcomes / Number of total outcomes
In this case, the favorable outcome is a left-handed woman and the total outcome is any woman.
The probability that a randomly selected person is a left-handed, given that she is a woman can be calculated as:
Probability = (Number of left-handed women) / (Number of total women)
Probability = 50 / 475
This calculates to approximately 0.105 (rounded to 3 decimal places).
Therefore, the probability that a randomly selected person is left-handed, given that she is a woman, is 0.105.