Answer:
P = 0.273
Explanation:
The probability to get exactly 4 heads can be calculated using the binomial distribution because we have n identical events with a probability p of success. So, we can use the following equation:
[tex]P(x)=\text{nCx }\cdot p^x\cdot(1-p)^{n-x}[/tex]Where n is the number of times that the coin is tossed, x is the number of heads and p is the probability to land heads.
Additionally, nCx is calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, replacing n by 8, x by 4, and p by 0.5, we get:
[tex]8C4=\frac{8!}{4!(8-4)!}=70[/tex][tex]\begin{gathered} P(4)=70\cdot0.5^4\cdot(1-0.5)^{8-4} \\ P(4)=70\cdot0.5^4\cdot0.5^4 \\ P(4)=0.273 \end{gathered}[/tex]Therefore, the probability that the coin will land heads 4 times is 0.273
