### 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 […]

### 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, […]

### How many different 7 card hands can be chosen from a standard 52 card deck?

This question aims to find how seven standard cards can be chosen from a deck of fifty-two cards. Combination can be used to find the number of ways in which 7 hand cards can be chosen from a set of 52 card decks as the order is not specified. Combination is the number of possible ways […]

### Suppose S and T are mutually exclusive events P(S)=20.

This question aims to find the P (S) or P (T) of two mutually exclusive events S and T if the probability of P (S) is given. Two events are called mutually exclusive if they do not occur at the same time or simultaneously. For Example, when we toss a coin, there are two possibilities […]