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.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

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the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!