Question

Based on the 2017 season, the Houston Astros have a winning percentage of 623. Use the binomial model to find the probability that the Astros will win 4 of their next 6 games. P (1) = ( z Xn-3) p'ai O A 12.4% O B. 24.7% O C. 32.1% O D. 62.3%

Answer 1

`p(x)=\lbrack(n!)/(x!(n-x)!)\rbrack p^x(1-p)^(n-x)`
`\begin{gathered} In\text{ this case,} \\ p=0.623 \\ n=6 \\ x=4 \end{gathered}`
`\begin{gathered} \text{HENCE} \\ p(4)=\lbrack(6!)/(4!(6-4)!)\rbrack0.623^4(1-0.623)^(6-4) \\ p(4)=\lbrack(6!)/(4!(2)!)\rbrack0.623^4(1-0.623)^2 \end{gathered}`
`\begin{gathered} \\ p(4)=\lbrack(720)/(24\cdot2)\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack(720)/(48)\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack15\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack15\rbrack(0.1506)(0.1421)^{} \\ p(4)=\lbrack15\rbrack(0.1506)(0.1421) \\ p(4)=0.321 \end{gathered}`
`\begin{gathered} \text{hence, the probability in percentage is} \\ 0.321\cdot100=32.1\text{ percent} \end{gathered}`