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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