Answer:
In the Explanation
Step-by-step explanation:
(a)From the attached probability tree, the possible outcomes are:
RR,RP,RG,RB,PR,PP,PG,PB,GR,GP,GB,GG,BR,BP,BG,BB
(b)Probability Distribution of Drawing Pink Marbles
1 answer:
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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
We have been given a graph of function g(x) which is a transformation of the function
Now we have to find the equation of g(x)
Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.
First you should check the graph of
You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.
Now the given graph has asymptote at x=-2
which is just 2 unit down from the original asymptote x=0
so that means we need shift f(x), 2 unit down hence we get:
but that will disturb the y-intercept (0,1)
if we multiply by 3 again then the y-intercept will remain (0,1)
Hence final equation for g(x) will be:
