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 […]

# Category Archives: Probability Q&A

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. […]

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 […]

– 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 […]

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 […]

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 […]

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 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 ${x>20}$. […]

– 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? […]

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 […]

– $ P (z space leq space – space 1.0 )$ – $ P (z space geq space – space 1 )$ – $ P (z space geq space – space 1.5 )$ – $ P ( – space 2.5 space geq space space z )$ – $ P (- space 3 space < space […]

This problem aims to build our understanding of random events and their predictable outputs. The concepts behind this problem are primarily associated with a probability and probability distribution. We can define probability as a way to indicate the occurrence of an unanticipated event, and the probability can be between zero and one. It estimates the […]

This problem aims to familiarize us with random events and their predictable outcomes. The concepts required to solve this problem are mostly related to probability, and probability distribution. So probability is a method to predict the occurrence of a random event, and its value can be between zero and one. It measures the likelihood of […]

begin{equation*}f(x,y)=left{begin{array}{ll}xe^{-x(1+y)}&quad xgeq 0space andspace ygeq 0 \ 0 &quad otherwiseend{array}right.end{equation*} Find the probability that the lifetime X of the first component exceeds 3. Find the marginal probability density functions. Find the probability that the lifespan of at most one component surpasses 5 This problem aims to familiarize us with probability and statistics. The concepts required to solve […]

This article aims to determine the probability of holding $3$ aces in a poker hand of $5$. The article uses the background concept of probability and combination. To solve problems like this, the idea of combinations should be clear. A combination combines $n$ things $k$ at once without repetition. The formula to find the combination is: [binom […]

b( 3, 8, 0.6 ) b( 5, 8, 0.6 ) P( 3 $le$ X $le$ 5 ) when n = 8 and p = 0.6 The aim of this question is to use the binomial random variable and its probability mass function to find probability values. The binomial probability mass function is mathematically defined as: […]

[ 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 […]

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, […]