activity 5.3 calculating expected value in the second round of the game show, you are offered another…

activity 5.3 calculating expected value in the second round of the game show, you are offered another choice. the host gives you $300. you can choose to keep the money or give the money back and spin the wheel shown to determine your winnings. all the sections on the wheel are equal in size. 1. calculate the expected value for one spin of the wheel. 2. should you keep the $300 or spin the wheel? explain your reasoning.

activity 5.3 calculating expected value in the second round of the game show, you are offered another choice. the host gives you $300. you can choose to keep the money or give the money back and spin the wheel shown to determine your winnings. all the sections on the wheel are equal in size. 1. calculate the expected value for one spin of the wheel. 2. should you keep the $300 or spin the wheel? explain your reasoning.

Answer

Explanation:

Step1: Identificar las probabilidades

Como todas las secciones del rodillo son iguales en tamaño, la probabilidad de caer en cada sección es $\frac{1}{8}$.

Step2: Calcular el valor esperado

El valor esperado $E(X)$ se calcula como $E(X)=\sum_{i = 1}^{n}x_ip_i$, donde $x_i$ son los valores posibles y $p_i$ son las probabilidades correspondientes. Aquí, $x_1 = 100$, $x_2 = 100$, $x_3 = 200$, $x_4 = 500$, $x_5 = 600$, $x_6 = 700$, $x_7 = 400$, $x_8 = 300$ y $p_1=p_2=p_3=p_4=p_5=p_6=p_7=p_8=\frac{1}{8}$. [ \begin{align*} E(X)&=\frac{1}{8}(100 + 100+200 + 500+600 + 700+400 + 300)\ &=\frac{1}{8}(2900)\ &= 362.5 \end{align*} ]

Answer:

  1. El valor esperado para un giro del rodillo es $$362.5$.
  2. Deberías girar el rodillo porque el valor esperado del giro ($$362.5$) es mayor que los $$300$ que tienes en mano actualmente.