Answer:
P(B|A)=0.25 , P(A|B) =0.5
Step-by-step explanation:
The question provides the following data:
P(A)= 0.8
P(B)= 0.4
P(A∩B) = 0.2
Since the question does not mention which of the conditional probabilities need to be found out, I will show the working to calculate both of them.
To calculate the probability that event B will occur given that A has already occurred (P(B|A) is read as the probability of event B given A) can be calculated as:
P(B|A) = P(A∩B)/P(A)
= (0.2) / (0.8)
P(B|A)=0.25
To calculate the probability that event A will occur given that B has already occurred (P(A|B) is read as the probability of event A given B) can be calculated as:
P(A|B) = P(A∩B)/P(B)
= (0.2)/(0.4)
P(A|B) =0.5
Answer:
1159
Step-by-step explanation:
She wants to read 1000 pages per week for five weeks.
So in total she wants to read 1000 * 5 = 5000 pages.
The first three weeks she read 894 pages per week.
So during the first three weeks she read a total of 894 * 3 = 2682 pages.
We want to find how many pages she must read per week for the last two weeks to reach her goal.
Goal: 5000 pages
Pages read so far: 2682
Weeks remaining: 2
To find how many pages she must read for the last two weeks we simply subtract the number of pages she read during the first 3 weeks (2682 ) by her goal ( 5000 )
5000 - 2682 = 2318
So she must read 2318 pages during the last 2 weeks.
If we want to find the amount of pages she must read per week during the last 2 weeks to reach her goal, we simply divide the amount of pages she must read during the last few weeks to reach her goal ( 2318 ) by the number of remaining weeks ( 2 )
2318 / 2 = 1159
So for the last two weeks she must average 1159 pages per week.
Condition (A) P(B/A) = y is true.
<h3>
What is probability?</h3>
- Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.
To find the true condition:
If two events are independent, then:
Use formulas for conditional probabilities:
- Pr(A/B) = Pr(A∩B) / Pr(B)
- Pr(B/A) = Pr(B∩A) / Pr(A)
For independent events these formulas will be:
- Pr(A/B) = Pr(A∩B) / Pr(B) = Pr(A) . Pr(B) / Pr(B) = Pr(A)
- Pr(B/A) = Pr(B∩A) / Pr(A) = Pr(B) . Pr(A) / Pr(A) = Pr(B)
Now in your case, Pr(A) = x and Pr(B) = y.
- Pr(A/B) = x, Pr(B/A) = y, Pr(A∩B) = x.y
Therefore, condition (A) P(B/A) = y is true.
Know more about probability here:
brainly.com/question/25870256
#SPJ4
The complete question is given below:
The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?
a. P(B|A) = y
b. P(A|B) = y
c. P(B|A) = x
d. P(A and B) = x + y
e. P(A and B) = x/y
