### What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?

This question aims to find the variance of the number of times a $6$ appears when a fair die is rolled $10$ times. We are surrounded by randomness. Probability theory is the mathematical concept that enables us to rationally analyze the chance of occurrence of an event. A probability of an event is a number […]

### In how many ways can 8 people be seated in a row if:

No seating restrictions. A and B sit together? 4 men and 4 women and no 2 men or 2 women can sit together? 5 men must sit together? 4 married couples must sit together? The aim of this problem is to introduce us to probability and distribution. The concepts required to solve this problem are related to introductory algebra and statistics. Probability is […]

### A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by the following function. What is the probability that the system functions for at least 5 months?

[ f(x) = left{ begin {array} ( Cx e^{-x/2} & x gt 0 \ 0 & xleq 0 end {array} right. ] The question aims to find the probability of a function for 5 months whose density is given in units of months. The question depends on the concept of Probability Density Function (PDF). The PDF […]

### In how many different orders can five runners finish a race if no ties are allowed?

The purpose of this question is to understand the concepts of permutations and combinations for evaluating a different number of possibilities of a given event. The key concepts used in this question include Factorial, Permutation and Combination. A factorial is a mathematical function represented by the symbol ! that operates only on the positive integers. In fact, […]

### If a and b are mutually exclusive events with p(a) = 0.3 and p(b) = 0.5, then p(a ∩ b) =

An experiment yields four results, each with $P ( E_1 ) = 0.2$, $P ( E_2 ) = 0.3$ and $P ( E_3 ) = 0.4$. What is the probability of $E_4$? An experiment yields four results, each with $P ( E_1 ) = 0.2$, \$ […]