Question

O PROBABILITYProbabilities of draws with replacementTry AgainA fair die is rolled 4 times. What is the probability of(If necessary, consult a list of formulas.)0X?

Answer 1

draws with replacement means that each event has an equal chance of occurence

A fair die has 6 faces (faces 1, 2, 3, 4, 5 & 6)

probability of choosing face 1 on all 4 rolls:

First roll

Pr (1) = number of face 1 / Total number of faces

Pr (1) = 1/6

Second roll

Pr (2) = number of face 1 / Total number of faces

Pr (2) = 1/6

Third roll

Pr (3) = number of face 1 / Total number of faces

Pr (3) = 1/6

Fourth roll

Pr (4) = number of face 1 / Total number of faces

Pr (4) = 1/6

Pr (face 1) for the 4 rolls = Pr (1) * Pr (2) * Pr (3) * Pr (4)

`Pr\text{ = (}(1)/(6))^4\text{ = }(1)/(1296)\text{ = 0.000772}`

Probability of rolling 1 the 4 times = 0.0772%