Ex 13.5, 6

Transcript

Ex 13.5, 6 A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0? Let X : be the number marked on bulb drawn Picking balls is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒﷮𝒏−𝒙﷯ 𝒑﷮𝒙﷯ n = number of times we pick the bulb = 4 p = Probability of getting digit 0 = 1﷮10﷯ q = 1 – p = 1 – 1﷮10﷯ = 9﷮10﷯ Hence, P(X = x) = 4Cx 𝟏﷮𝟏𝟎﷯﷯﷮𝒙﷯ 𝟗﷮𝟏𝟎﷯﷯﷮𝟒−𝒙﷯ We need to find Probability that none is marked with 0 i.e. P(X = 0) P(X = 0) = 4C0 1﷮10﷯﷯﷮0﷯ 9﷮10﷯﷯﷮4 −0﷯ = 4 !﷮ 4 − 0﷯ ! 0 !﷯ ×1 × 9﷮10﷯﷯﷮4﷯ = 4 !﷮4 !﷯ × 9 ﷮4﷯﷮ 10﷮ 4﷯﷯ = 9 ﷮4﷯﷮ 10﷮ 4﷯﷯ = 𝟗﷮𝟏𝟎﷯﷯﷮𝟒﷯