Question

a) A six sided dice is unbiased . It is numbered 1,2,3,4,5 and 6 on its faces. The dice is rolled several times until it lands on the number 5. Find the probability that this happens on the fifth roll. Show proper working and explanation).

Answer 1

P(not 5) =5/6 and P(5) = 1/6
If the first 5 is rolled on the 5th roll then the first four rolls were not 5
P(5 on fifth roll) = 5/6 x 5/6 x 5/6 x 5/6 x 1/6 = 5^4/6^5 = 625/7776 = 0.080375...