Consider the sample space S = {1, 2, 3, . . ., 10}. Let A = all odd numbers in S. Let B = all multiples of 5 in S. Compute P(B | A). Enter your answer as a fraction using the "/" and do not include spaces in your answer.
A={1,3,5,7,9}
B={5,10}
A∩B={5}
Assuming random sampling,
P(B)=|B|/|S|=2/10=1/5
P(A)=|A|/|S|=5/10=1/2
P(A∩B)=1/10
Finally,
P(B|A)=P(B∩A)/P(A) (by definition)
I'll let you take it from here.
actually it's 2/10
To compute P(B | A), we need to find the probability of event B occurring given that event A has occurred. In other words, we need to find the probability of getting a multiple of 5 from the set of odd numbers.
First, let's identify the odd numbers in the sample space S. From 1 to 10, the odd numbers are {1, 3, 5, 7, 9}.
Next, let's find the multiples of 5 in the sample space S. From 1 to 10, the multiples of 5 are {5, 10}.
To compute the probability of event B occurring given that event A has occurred, we need to find the intersection of events A and B (i.e., the numbers that are both odd and multiples of 5). In this case, their intersection is {5}.
The probability of event B occurring given that event A has occurred can be calculated as the number of outcomes in the intersection divided by the number of outcomes in event A.
So, P(B | A) = (number of outcomes in the intersection) / (number of outcomes in event A) = 1/5.
Therefore, the answer is 1/5.