Split 63 into the ratio 4:3
2 answers:
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Answer:
b) No, it's not independent.
c) 0.02
d) 0.59
e) 0.57
f) 0.5616
Step-by-step explanation:
To answer this problem, a Venn diagram should be useful. The diagram with the information of Event 1 and Event 2 is shown below (I already added the information for the intersection but we're going to see how to get that information in the b) part of the problem)
Let's call A the event that she passes the first course, then P(A)=.73
Let's call B the event that she passes the second course, then P(B)=.66
Then P(A∪B) is the probability that she passes the first or the second course (at least one of them) is the given probability. P(A∪B)=.98
b) Is the event she passes one course independent of the event that she passes the other course?
Two events are independent when P(A∩B) = P(A) * P(B)
So far, we don't know P(A∩B), but we do know that for all events, the next formula is true:
P(A∪B) = P(A) + P(B) - P(A∩B)
We are going to solve for P (A∩B)
.98 = .73 + .66 - P(A∩B)
P(A∩B) =.73 + .66 - .98
P(A∩B) = .41
Now we will see if the formula for independent events is true
P(A∩B) = P(A) x P(B)
.41 = .73 x .66
.41 ≠.4818
Therefore, these two events are not independent.
c) The probability she does not pass either course, is 1 - the probability that she passes either one of the courses (P(A∪B) = .98)
1 - P(A∪B) = 1 - .98 = .02
d) The probability she doesn't pass both courses is 1 - the probability that she passes both of the courses P(A∩B)
1 - P(A∩B) = 1 -.41 = .59
e) The probability she passes exactly one course would be the probability that she passes either course minus the probability that she passes both courses.
P(A∪B) - P(A∩B) = .98 - .41 = .57
f) Given that she passes the first course, the probability she passes the second would be a conditional probability P(B|A)
P(B|A) = P(A∩B) / P(A)
P(B|A) = .41 / .73 = .5616
Answer:
1250
Step-by-step explanation:
We are given that the playground is fenced on three sides of the playground and the four side has an existing wall.
Let the length of the rectangle be 'X' feet and width be 'Y' feet.
As the fencing is done using 100 feet of fence. We get the relation between the sides and the fence as, X + 2Y = 100.
As, X + 2Y = 100 → X = 100 - 2Y
Now, the area of the rectangle = XY = X × ( 100 - 2Y ).
i.e Area of the rectangle = .
The general form of a quadratic equation is .
The maximum value of a quadratic equation is given by .
Therefore, the greatest value of is at Y =
=
= 25.
Thus, Y = 25 and X = 100 - 2Y → X = 100 - 2 × 25 → X = 50.
Hence, the area of the rectangle is XY = 50 × 25 = 1250 .