List of top Applied Mathematics Questions on Probability

The mortality rate for a certain disease is 0.007. Using Poisson distribution, calculate the probability for 2 deaths in a group of 400 people. [Use $e^{-2.8} = 0.0608$]

Two numbers are selected at random (without replacement) from the first six positive integers. Let $X$ denote the smaller of the two numbers obtained. Calculate the mathematical expectation of $X$.

If a random variable \( X \) has the probability distribution:
\[ P(X = x) = \begin{cases} k, & \text{if } x = 0 \\ 2k, & \text{if } x = 1 \text{ or } 2 \\ 0, & \text{otherwise} \end{cases} \] then the value of \( k \) is