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)
[tex]Pr\text{ = (}\frac{1}{6})^4\text{ = }\frac{1}{1296}\text{ = 0.000772}[/tex]Probability of rolling 1 the 4 times = 0.0772%
