Question

What is the probability of throwing 6 with a dice at least once in 3 attempt?

Answer 1

The probablity of getting atleast one 6 in 3 throw of die is

Probability of getting one 6 + Probability of getting two 6's + Probab of getting 3 6's

let probab of getting 6 is P(6) = 1/6

let probab of NOT getting 6 is P(6'') = 5/6

Probab of getting only one 6 = P(6)*P(6'')*P(6'') + P(6")*P(6)*P(6'') + P(6'')*P(6'')*P(6)

probab of getting only one 6 = 3*(1/6)*(5/6)*(5/6) = 75/216

Probab of getting only two 6 = P(6)*P(6)*P(6'') + P(6")*P(6)*P(6) + P(6)*P(6'')*P(6)

Probab of getting only two 6 = 3*(1/6)*(1/6)*(5/6) = 15/216

Probab of getting all three 6 = P(6)*P(6)*P(6) + P(6)*P(6)*P(6) + P(6)*P(6)*P(6)

Probab of getting all three 6 = 3*(1/6)*(1/6)*(5/6) = 3/216

The probablity of getting atleast one 6 in 3 throw of die is

(3+15+75)/216 = 31/72