At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer: 9/20
=============================================================
Explanation:
Define the following events
- D = weather is dry
- R = weather is rainy
- S = weather is snowy
- L = person is late
- T = person is on time
We are given the following probabilities
- P(D) = 1/2
- P(R) = 1/3
- P(S) = 1/6
Then we're further told that "if it is dry, then the probability someone will arrive on time is 4/5". We can condense that into the notation
P(T given D) = 4/5
The "given D" means that we know 100% that event D has occurred. So we're seeing how event T behaves because of D occurring. In other words P(T given D) is the same as saying "What is P(T) when we know D has happened?"
-------------------------
The instructions also mention that "If it rains, the probability someone is on time is 2/5" tells us we have the notation
P(T given R) = 2/5
And also, the probability someone is on time if it is snowy is
P(T given S) = 1/10
due to it saying "If it snows, the probability that someone will arrive on time is 1/10".
-------------------------
To recap so far, your teacher told you these three conditional probabilities
- P(T given D) = 4/5
- P(T given R) = 2/5
- P(T given S) = 1/10
They are conditional due to the "given" as part of the probability. They depend on the given event happening.
Subtract each fraction from 1 and we end up with these complementary probabilities
- P(L given D) = 1/5
- P(L given R) = 3/5
- P(L given S) = 9/10
I'm using the idea that P(A)+P(B) = 1, where A and B are complementary events. One or the other event must happen. Either you are on time, or you are late.
---------------------------
Recall the conditional probability formula is
P(A given B) = P(A and B)/P(B)
which rearranges to
P(A and B) = P(A given B)*P(B)
We'll use this idea to get the following
- P(L and D) = P(L given D)*P(D) = (1/5)*(1/2) = 1/10
- P(L and R) = P(L given R)*P(R) = (3/5)*(1/3) = 1/5
- P(L and S) = P(L given S)*P(S) = (9/10)*(1/6) = 3/20
This means,
P(L) = P(L and D) + P(L and R) + P(L and S) ..... law of total probability
P(L) = 1/10 + 1/5 + 3/20
P(L) = 2/20 + 4/20 + 3/20
P(L) = (2+4+3)/20
P(L) = 9/20 is the probability someone is late
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
