Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel which returns him to his cell after two days travel. the second door leads to a tunnel that returns him to his cell after three days travel. the third door leads immediately to freedom.
(a) assuming the prisoner will always select doors 1, 2 and 3 with probabilities 0.5, 0.3 and 0.2 respectively, what is the expected number of days until he reaches freedom?
(b) calculate the variance of the number of days until the prisoner reaches freedom.

associative property hopes this ! : )

step-by-step explanation:

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d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

hi there!

the answer will be d: 2