Question

An instant lottery game gives you probability 0.03 of winning on any one play. Plays are independent of each other. If you are to play four times in a row, the probability that you do not win in any of the four consecutive plays is about: (Answer as a decimal rounded to three decimal places)

Answer 1

Probability of winning the game in a single play (p) = 0.03

Number of plays (n) = 4

Probability of failure in a single game (q) = 1 - p = 1 - 0.03 = 0.97

Let X be a random variable representing the number of wins.

Now X ~ N( n = 4, p = 0.03)

P(X = x) =

Probability of not winning in any of the four consecutive plays is given as P(X = 0).

P(X = 0) = =   = (0.97)⁴ = 0.8852 0.885

Hence, probability of not winning in any of the four consecutive plays is 0.885

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