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:
[tex]P(x)=(^n_x)p^xq^{n-x}[/tex]
Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials
Combination Formula:
[tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]
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:
[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]
Rewrite 0.50 as a fraction
[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]
Cancel out values in fraction, and also square the fraction
[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]
Multiply fractions
[tex]P(x)=3*\frac{1}{8}[/tex]
Multiply the two values
[tex]P(x)=\frac{3}{8}[/tex]
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
