type the correct answer in each box. jackson goes to the gym 0, 2, or 3 days per week, depending on work…

type the correct answer in each box. jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. the expected value of the number of days per week that jackson goes to the gym is 2.05. the probability that he goes 0 days is 0.1, the probability that he goes 2 days is blank, and the probability that he goes 3 days is blank.

type the correct answer in each box. jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. the expected value of the number of days per week that jackson goes to the gym is 2.05. the probability that he goes 0 days is 0.1, the probability that he goes 2 days is blank, and the probability that he goes 3 days is blank.

Answer

Explanation:

Step1: Let the probabilities be variables

Let the probability that he goes 2 days be $p_2$ and the probability that he goes 3 days be $p_3$. We know that the sum of all probabilities is 1, so $0.1 + p_2 + p_3=1$, which simplifies to $p_2 + p_3 = 0.9$. The formula for expected - value $E(X)$ is $E(X)=\sum_{i}x_ip_i$. Here, $x_0 = 0$, $x_2 = 2$, $x_3 = 3$, and $E(X)=2.05$. So, $E(X)=0\times0.1+2p_2 + 3p_3=2.05$, which simplifies to $2p_2+3p_3=2.05$.

Step2: Solve the system of equations

From $p_2 + p_3 = 0.9$, we have $p_3 = 0.9 - p_2$. Substitute $p_3 = 0.9 - p_2$ into $2p_2+3p_3=2.05$. We get $2p_2+3(0.9 - p_2)=2.05$. Expand the left - hand side: $2p_2 + 2.7-3p_2=2.05$. Combine like terms: $-p_2=2.05 - 2.7=-0.65$. So, $p_2 = 0.65$.

Step3: Find the other probability

Since $p_2 + p_3 = 0.9$ and $p_2 = 0.65$, then $p_3=0.9 - 0.65 = 0.25$.

Answer:

0.65, 0.25