Tina works on 5 projects. The probability of completing a project on schedule is 3/7. What is the probability that she will complete at least 3 projects on schedule?
The answer is about 36.79%
How do you solve this can some one show me in steps please?
The answer is about 36.79%
How do you solve this can some one show me in steps please?
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P(atleast 3) = P(3) + P(4) + P(5)
n=5 ; p=3/7 ; q=4/7
p(3) = 5c3 * (3/7)^3 * (4/7)^2
p(3) = 5c4 * (3/7)^4 * (4/7)
p(3) = 5c5 * (3/7)^5
P(atleast 3) = [4320+1620+243]/16807
=6183/16807
=0.36788
=36.78%
---------------------------------------…
q = 1-p
=1-(3/7)
=4/7
n=5 ; p=3/7 ; q=4/7
p(3) = 5c3 * (3/7)^3 * (4/7)^2
p(3) = 5c4 * (3/7)^4 * (4/7)
p(3) = 5c5 * (3/7)^5
P(atleast 3) = [4320+1620+243]/16807
=6183/16807
=0.36788
=36.78%
---------------------------------------…
q = 1-p
=1-(3/7)
=4/7
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Let's take it one step at a time:
We want to know what the probability is that Tina will complete 3, 4 or 5 projects on time.
The probability of her completing each project on time is 3/7.
The probability of her not completing each project on time is 4/7.
The probability of completing at least 3 projects on time is the probability of completing 3 on time + the probability of completing 4 on time + the probability of completing 5 on time.
The probability of her completing 5 projects on time is (3/7) ^5 = 3^5 / 7^5 = 243 / 16807
Now, if she is going to complete 4 projects on time, she could fail on one. That on could be any of the 5 projects.
The probability of her completing the first 4 on time and failing at the last project is:
3/7 x 3/7 x 3/7 x 3/7 x 4/7
= (3/7)^4 x (4/7)^1
= 324 / 16807
Now, to get the total probability that she will complete 4 of the five on time, multiply 324 / 16807 by 5 and get: 1620 / 16807
Next, find the probability that Tina will complete exactly 3 projects on time.
She could complete the first 3 and fail at the last two: (3/7)^3 x (4/7)^2 = 432 / 16807.
If S = Success and F = failure, that could be expressed as:
S S S F F .
If we know how many ways three S's and two F's could seated in five spots, then we could multiply that by 432 / 16807 to get the probability of exactly 3 S's and 2 F's.
We want to know what the probability is that Tina will complete 3, 4 or 5 projects on time.
The probability of her completing each project on time is 3/7.
The probability of her not completing each project on time is 4/7.
The probability of completing at least 3 projects on time is the probability of completing 3 on time + the probability of completing 4 on time + the probability of completing 5 on time.
The probability of her completing 5 projects on time is (3/7) ^5 = 3^5 / 7^5 = 243 / 16807
Now, if she is going to complete 4 projects on time, she could fail on one. That on could be any of the 5 projects.
The probability of her completing the first 4 on time and failing at the last project is:
3/7 x 3/7 x 3/7 x 3/7 x 4/7
= (3/7)^4 x (4/7)^1
= 324 / 16807
Now, to get the total probability that she will complete 4 of the five on time, multiply 324 / 16807 by 5 and get: 1620 / 16807
Next, find the probability that Tina will complete exactly 3 projects on time.
She could complete the first 3 and fail at the last two: (3/7)^3 x (4/7)^2 = 432 / 16807.
If S = Success and F = failure, that could be expressed as:
S S S F F .
If we know how many ways three S's and two F's could seated in five spots, then we could multiply that by 432 / 16807 to get the probability of exactly 3 S's and 2 F's.
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