Probabilities are used to determine the chances of Laura winning an activity
- The value of p is 1/12
- The expected score of the game is -1/6
- The probability that she has a total score of 5 after two rounds is 0
How to calculate the value of p
To calculate the value of p, we make use of the following probability formula
[tex]\sum P(x) = 1[/tex]
So, we have:
[tex]\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + p + \frac 1{12} = 1[/tex]
Collect like terms
[tex]\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + \frac 1{12} + p= 1[/tex]
Evaluate the sums, on the left-hand side
[tex]\frac{11}{12} + p = 1[/tex]
Subtract 11/12 from both sides
[tex]p = \frac 1{12}[/tex]
Hence, the value of p is 1/12
(b) How to calculate the expected score
This is calculated using the following expected value formula
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = -3 * \frac{3}{12} -1 * \frac 1{12} + 0 * \frac 4{12} + 1 * \frac 2{12} + 2 * \frac 1{12} + 4 * \frac 1{12}[/tex]
Evaluate the products
[tex]E(x) = -\frac{9}{12} - \frac 1{12} + \frac 2{12} + \frac 2{12} + \frac 4{12}[/tex]
[tex]E(x) = -\frac 2{12}[/tex]
Simplify
[tex]E(x) = -\frac 1{6}[/tex]
Hence, the expected score of the game is -1/6
(c) The probability that she has a total score of 5 after two rounds
From the table, we have:
[tex]P(5) = 0[/tex]
For after two rounds, we make use of the following equation
[tex]P(5) * P(5) = 0 * 0[/tex]
[tex]P(5) * P(5) = 0[/tex]
Hence, the probability that she has a total score of 5 after two rounds is 0
Read more about probabilities at:
https://brainly.com/question/25870256
