The average number of radioactive particles passing through a counter during 1 millisecond in a lab experiment is 4. What is the probability that more than 2 milliseconds pass between particles?
One side of a triangle is three times the shortest side. The third side is 7 feet more than the shortest side. The perimeter is 62 feet. Find all three sides.
x= shortest side
3x= side one
x+7 = third side
then you add all these together and set them equal to 62 and solve for x.
To calculate the probability of more than 2 milliseconds passing between particles, we need to determine the waiting time between particles.
The average number of particles passing through the counter in 1 millisecond is 4. This means that the average time between particles is 1/4 milliseconds.
To find the probability that more than 2 milliseconds pass between particles, we can use the exponential distribution formula:
P(X > t) = e^(-λt)
where:
- P(X > t) is the probability that the waiting time between particles is greater than t,
- λ is the rate parameter (equal to the average number of particles per unit of time), and
- t is the given time interval.
In this case, λ = 1/(1/4) = 4 and t = 2 milliseconds.
Substituting these values into the formula:
P(X > 2) = e^(-4*2)
= e^(-8)
Using a scientific calculator or math software, we can find that e^-8 is approximately 0.00033546.
Therefore, the probability that more than 2 milliseconds pass between particles is approximately 0.00033546.