On rainy days, Joe is late to work with probability .3; on nonrainy days, he is late with probability .1. With probability .7, i
1 answer:
Answer:
a) 76% probability that Joe is early tomorrow.
b) 64.47% conditional probability that it rained
Step-by-step explanation:
We have these following probabilities:
A 70% probability that it will rain tomorrow.
A 30% probability that it does not rain tomorrow.
If it rains, a 30% probability that Joe is late and a 100-30 = 70% probability that Joe is early.
if it does not rain, a 10% probability that Joe is late and a 100-10 = 90% probability that Joe is early.
(a) Find the probability that Joe is early tomorrow.
Either it rains(70% probability) and he is early(70% probability when it rains), or it does not rain(30% probability) and he is early(90% probability when it does not rain). So
76% probability that Joe is early tomorrow.
(b) Given that Joe was early, what is the conditional probability that it rained?
By the Bayes theorem, this probability is:
The probability that it rained and he was early divided by the probability he was early.
Rained and early
70% probability it rains.
70% probability he is early when it rains.
Early
From a), 0.76
Probability
64.47% conditional probability that it rained
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Answer:
The given series converges and
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be:
Hence,