Question

Four spinners are spun. Spinner 1 has outcomes Spinner 2 has outcomes Spinner 3 has outcomes Spinner 4 has outcomes The outcomes for each spinner are equally likely. is the sum of the numbers that come up on the spinners. What is the expected value of

Answer 1

Complete Question

Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?

Answer:

$E(s)=14.5$

Step-by-step explanation:

From the question we are told that:

Spinner 1 ={1,2,3,4,5,6,7,8}

Spinner 2=  {1,2,3,4,5,6}

Spinner 3 = {1,2,3,4,5,6}

Spinner 4  {1,2,3,4,5}

Generally the equation for expected outcome is mathematically given by

$E(s)=\sum P(x).x$

Where

$x=\frac{n(n+1)}{2}$

For Spinner 1

$E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}$

$E(s_1)=4.5$

For Spinner 2

$E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}$

$E(s_2)=3.5$

For Spinner 3

$E(s_2)=E(s_3)$

For Spinner 3

$E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}$

$E(s_4)=3$

Therefore The Expected Value

$E(s)=\sum E(s 1..4)$

$E(s)=4.5+2(3.5)+3$

$E(s)=14.5$