Question

An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. What is the probability that the first and second balls will be a 8?

Answer 1

Answer:

The probability is:

                   $\dfrac{1}{400}$

Step-by-step explanation:

It is given that:

An urn contains balls numbered 1 through 20.

A ball is chosen, returned to the urn, and a second ball is chosen.

This means that this is a case of a replacement.

Hence, one of the event is independent of the other.

Now we know that the probability to get a particular number of ball is:

                  $\dfrac{1}{20}$

( Since, there are total 20 balls and a ball of one particular number is just unique )

i.e. $\text{Probability of getting a 8}=\dfrac{1}{20}$

Hence, the probability that the first and second balls will be a 8 is:

$=\dfrac{1}{20}\times \dfrac{1}{20}\\\\\\=\dfrac{1}{400}$

Answer 2

An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. The probability that the first and second balls will be a 8 is  $\frac{1}{400}$

Further explanation

A random variable, random quantity, aleatory variable, or stochastic variable is described as a variable that the values depend on outcomes of a random phenomenon. The formal mathematical treatment of random variables is a topic in probability theory

There are two types of random variables such as discrete and continuous. Random variables can assume only a countable number of values are called discrete. Whereas the random variables that can take on any of the countless number of values in an interval are called continuous.

The chance of the first ball being a $8$ is $\frac{1}{20}$. Similarly, the chance of the second being a $8$ is $\frac{1}{20}$.

To find the chance if both happening, muliply the two.  

$\frac{1}{20}$ *   $\frac{1}{20}$  = $\frac{1}{400}$

Because since you return it  $\frac{1}{20}$  again and those combined make  $\frac{1}{400}$  since $20 * 20= 400$

Learn more

1. Learn more about urn brainly.com/question/7153497
2. Learn more about probability  ball  brainly.com/question/3372562
3. Learn more about probability brainly.com/question/7965468

Answer details

Grade:  9

Subject:  mathematics

Chapter:  probability

Keywords: urn,  balls, probability, second, first