Suppose flaws occur on the surface of glass with density of 3 per square meter. What is the probability of there being exactly 4 flaws on a sheet of glass of area 0.5 square meter?
0.047
To find the probability of there being exactly 4 flaws on a sheet of glass, we can use the concept of a Poisson distribution. The Poisson distribution is often used to model the number of events that occur in a fixed interval of time or space.
In this case, we have a density of 3 flaws per square meter. The number of flaws on a sheet of glass follows a Poisson distribution with a mean of λ, where λ is given by the product of the density and the area.
Therefore, λ = 3 (flaws per square meter) * 0.5 (square meters) = 1.5.
The probability of having exactly 4 flaws on the sheet of glass can be calculated using the Poisson probability mass function (PMF):
P(x=k) = (e^(-λ) * λ^k) / k!
where P(x=k) is the probability of getting exactly k flaws, λ is the mean, e is Euler's number (approximately 2.71828), and k! is the factorial of k.
So, for k = 4:
P(x=4) = (e^(-1.5) * 1.5^4) / 4!
Calculating this expression will give you the probability of there being exactly 4 flaws on a sheet of glass with an area of 0.5 square meters.