Let's say the numbers are "a" and "b"
thus
set the derivative to 0, and check the critical points, there's only one anyway
and do a first-derivative test, to see if it's a maximum
Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.
<h3>What is the binomial distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 0.54% of the calls receive a busy signal, hence p = 0.0054.
- A sample of 1300 callers is taken, hence n = 1300.
The probability that at least 5 received a busy signal is given by:
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Then:
Then:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.
0.8295 = 82.95% probability that at least 5 received a busy signal.
More can be learned about the binomial distribution at brainly.com/question/24863377
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The probability that he first chooses an advanced book and then chooses a beginner book is 6/121.
<h3>Probability</h3>
Given:
Beginner book=2
Intermediate book=6
Instructional piano books=11
Advanced books=3
Hence:
Probability=(2×3)÷(11×11)
Probability=6/121
Therefore the probability that he first chooses an advanced book and then chooses a beginner book is 6/121.
Learn more about probability here: brainly.com/question/24756209
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Answer:
Step-by-step explanation:
<u>For every time you have a probability of getting 1 is:</u>
<u>For all 6, the probability of outcome of 1 is:</u>
- P(1x6) = (1/10)⁶ = 0.000001
1.001 is the smallest :)))
