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Answer:
Probability that a 20- cubic foot block of wood has at most 1 knot P (X<=1) = 0.5918
Step-by-step explanation:
Average rate of knot= 1.4
Wavelength = 1.4
Geometric probability is given by:
P(X= K) = wavelength ^k × e^-wavelegth
P(X=0) = (1.4^0 × e^-1.4)/0!
P(X=0) = 1 × 0.2466 = 0.2466
P(X=1) = 1.4^1 × e^-1.4
P(X=1)= 1.4×0.2466= 0.3452
P(X<=1)= P(X=0) + P(X=1)
P(X<=1) = 0.2466 + 0.3452 = 0.5918
Here is a simple way we can do this.
We have six blanks.
__ __ __ __ __ __
Now, we have 13 possible options to fill in blank number one.
13 __ __ __ __ __
Now we have 12 possible options to fill in blank number two because one person has already been chosen.
13 12 __ __ __ __
Now we have 11 possible options for blank number three.
13 12 11 __ __ __
Now we have 10 possible options for blank number four.
13 12 11 10 __ __
And so forth until we get:
13 12 11 10 9 8
Now we just have to multiply the numbers all together.
13 * 12 * 11 * 10 * 9 * 8
is equal to:
1235520 ways.
Answer: 50.26548 (50.27)
Step-by-step explanation:
Circumference = 2 x π x r(radius)
Diameter = 2 x r(radius)
C = π x 16 = 50.26548
