diff --git a/Oceanverse.md b/Oceanverse.md index a6bd024..b85c8a7 100644 --- a/Oceanverse.md +++ b/Oceanverse.md @@ -1403,24 +1403,24 @@ Thus, the probability of a dart hitting the shaded region is \( \frac{3}{4} \) o
65.A factory produces items, and each item is independently defective with probability -0.02. If 100 items are produced in a day, what is the expected number of defective items? +0.2. If 100 items are produced in a day, what is the expected number of defective items?
Sol. To find the expected number of defective items produced in a day by the factory, we use the concept of expectation in probability theory. Given: -- Each item is defective with probability \( p = 0.02 \). +- Each item is defective with probability \( p = 0.2 \). - The number of items produced in a day \( n = 100 \). The expected number of defective items \( E(X) \) can be calculated using the formula for the expectation of a binomial distribution: \[ E(X) = n \cdot p \] Substituting the given values: -\[ E(X) = 100 \cdot 0.02 \] -\[ E(X) = 2 \] +\[ E(X) = 100 \cdot 0.2 \] +\[ E(X) = 20 \] -Thus, the expected number of defective items produced in a day is 2. +Thus, the expected number of defective items produced in a day is 20.

66.A point is chosen at random inside a sphere of radius R. What is the probability that this point is closer to the center of the sphere than to its surface?