### Consider a binomial experiment with n=20 and p=0.70.

Find f(12). Find f(16). Find $P(x ge 16)$. Find $P(x le 15)$. Find $E(x)$. Find $var(x)$ and $sigma$. The main objective of this question is to find the binomial probability. This question uses the concept of the binomial distribution to find the binomial probability. In binomial distribution, we have the probability of two possible outcomes […]

### Can two events with nonzero probabilities be both independent and mutually exclusive?

The question aims to answer if two events can be both independent and mutually exclusive simultaneously with non-zero probabilities. When we toss two coins, the result of one coin does not affect the other. if one outcome is head/tail, this doesn’t affect the result of another event. This means mutually exclusive events are not independent. […]

### Based on the normal model N(100, 16), describing IQ scores. What percent of people’s IQ would you expect to be:

Percentage of population greater than 80. Percentage of population less than 90. Percentage of population between 112 – 132. The question aims to find the percentage of the people’s IQ with the mean of the population to be 100 and a standard deviation of 16. The question is based on the concepts of probability from […]

### A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment.

– The genetic trait was previously found to be 1 in every 8 frogs. – He collects 12 frogs and examines them for the genetic trait. – What is the probability the wildlife biologist would find the trait in the following batches if the trait frequency is the same? a) None of the frogs he […]

### Find the probability P (E or F), if E and F are mutually exclusive.

P(E) = 0.38 P(F) = 0.57 The of this question is to find the probability of two mutually exclusive events E and F when either of them can occur. The question is based on the concept of probability of mutually exclusive events. Two events are mutually exclusive events when both of these events do not […]

### A standard deck of cards contains 52 cards. One card is selected from the deck.

Compute the probability of randomly selecting a spade or diamond. P(spade or diamond) Compute the probability of randomly selecting a spade or diamond or heart. P(spade or diamond or heart) Compute the probability of randomly selecting a king or club. P(king or club) This question aims to find the probability of different cards from a […]

### If X is an exponential random variable parameter, λ = 1 , compute the probability density function of the random variable Y defined by Y = logX.

This problem aims to familiarize us with the probability density functions. The concepts required to solve this problem are continuous random variables and probability distributions, which include exponential distribution and densities of random variables. A probability density function or PDF is used in probability theory to describe the probability of a random variable staying within […]

### The probability density function of x the lifetime of a certain type of electronic device

The probability density function f(x) of a random variable x is given below, where x is the lifetime of a certain type of electronic device (measured in hours): [ f(x) =Bigg{begin{array}{rr} dfrac{10}{x^2} & x>10\ 0 & xleq 10 \ end{array}] – Find the cumulative distribution function $F(x)$ of $x$. – Find the probability that ${x>20}$. […]

### How many ways are there to choose four members of the club to serve on an executive committee?

– There are $25$ members in a club. – In how many ways can $4$ members be chosen to serve in an executive committee? – In how many ways can a president, vice president, secretary, and treasurer of the club be chosen so that each person can only hold a single office at a time? […]

### 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 […]

### 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, […]