Question

If dice are rolled what is probability that a six first appears on the 10th roll?

Answer 1

`P("first 6 appears on 10th roll")=(5^9)/(6^10)=0.0323011166`

Explanation:

`P("first 6 appears on 10th roll")`

`color(white)("XXX")=color(green)(P("6 did not appear on first 9 rolls"))xxcolor(blue)(P("6 appears on 10th roll"))`

`P("6 did not appear on a single roll")=5/6`

`color(green)(P("6 did not appear on 9 rolls in succession"))= color(green)((5/6)^9)`

`color(blue)(P("6 did appear on 10th roll"))=color(blue)(1/6)`

`:. P("first 6 appears on 10th roll")=color(green)((5^9)/(6^9))xxcolor(blue)(1/6)`

`color(white)("XXXXXXXXXXXXXXXXXXX")=(5^9)/(6^10)`

(use calculator to evaluate beyond this point if desired)