Question

Question: A coin is biased so that the probability a head comes up when it is flipped is 0.6. What is the expected number of heads that come up when it is flipped 10 times?

Short answer

Answer

The expected number of heads that come up it is flipped 10 times is 6.

Step-by-step solution

Given Information  

A coin is biased so that the probability a head comes up when it is flipped is 0.6

Definition of Integral and Integration  

Probability distribution Types: Discrete Probability distribution and Continuous probability distribution. They each define Discrete and Continuous random variables respectively.

Discrete Probability distribution gives the probability that a discrete random variable will have a specified value. Such a distribution will represent data that has a finite countable number of outcomes. The two conditions discrete probability distributions must satisfy are: \({\bf{0}}{\rm{ }} \le {\rm{ }}{\bf{P}}\left( {{\bf{X}}{\rm{ }} = {\rm{ }}{\bf{x}}} \right){\rm{ }} \le {\rm{ }}{\bf{1}}\)

• . This implies that the probability of a discrete random variable,\({\bf{X}}\), taking on an exact value,\({\bf{x}}\), lies between\({\bf{0}}\)and\({\bf{1}}\)

• \(\sum {\bf{P}}\left( {{\bf{X}}{\rm{ }} = {\rm{ }}{\bf{x}}} \right){\rm{ }} = {\bf{1}}\). The sum of all probabilities must be equal to\({\bf{1}}\)

Some commonly used Discrete probability distributions are Geometric distributions, binomial distributions and Bernoulli distributions

Calculation of the expected number of heads come up when it is flipped 10 times

Flipping biased coin is a Bernoulli trial.

If a head appearing is considered as success, the probability of success\(p = 0.6\)and

\(1 - p = 0.4.\)

The expected number of success for \(n\) Bernoulli trials is\(np\).

Here \(n = 10,p = 0.6,\)hence the expected number of heads that turn up is

\(\begin{array}{l}np = 10 \times 0.6\\ = 6\end{array}\)

Therefore, on flipping it 10 times the expected number of heads that come up is 6