Probability Q&A Archives - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day

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 […]

What is the probability that a fair die never comes up an even number when it is rolled six times?

This problem aims to find the probability of the occurrence of a random event and its predictable outcomes. The concepts required for this problem are mainly related to probability and the product rule. Let’s first look at a fair die, whose each face has the identical probability of coming faced up. The product rule is […]

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs?

– In existing experimentation, $100$ customers were asked to choose the design they liked. The subsequent data were acquired. Do the data demonstrate the thought that one design is just as conceivable to be designated as another? Explain. This problem aims to familiarize us with the concept of the null hypothesis and probability distribution. The […]