Question

Question 2: 11 pts

Answer 1

Answer:

3/8 or 0.375 or 37.5%

Step-by-step explanation:

So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3  combinations or 8 combinations. But we can also use Binomial Distribution Formula.

Binomial Distribution Formula:

   $P(x)=(^n_x)p^xq^{n-x}$

   Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials

   Combination Formula:

       $(^n_x) = \frac{n!}{x!(n-x)!}$

So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.

So let's plug the values into the equation:

$P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1$

Rewrite 0.50 as a fraction

$P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1$

Cancel out values in fraction, and also square the fraction

$P(x)=3*\frac{1}{4}*\frac{1}{2}$

Multiply fractions

$P(x)=3*\frac{1}{8}$

Multiply the two values

$P(x)=\frac{3}{8}$

This means the probability is 3/8 or 0.375 or 37.5%

I also provided a diagram on how to just draw out each scenario/combination