an instant lottery game gives you probability .02 of winning on any one play. Plays are indpendent of each other. If you play 5 times, what is the probability that you win at least once.

To find the probability of winning at least once when playing the instant lottery game 5 times, we can use the concept of complementary probability.

The complementary probability is the probability of the event not occurring. In this case, it means not winning at all in 5 plays.

First, let's calculate the probability of not winning on a single play. Since the winning probability is given as 0.02, the probability of not winning on one play is 1 - 0.02 = 0.98.

Since the plays are independent, the probability of not winning in all 5 plays is the product of the probabilities of not winning on each play. So, the probability of not winning in 5 plays is 0.98 * 0.98 * 0.98 * 0.98 * 0.98 = 0.9039207968.

To find the probability of winning at least once, we subtract the probability of not winning at all from 1. Therefore, the probability of winning at least once in 5 plays is 1 - 0.9039207968 = 0.0960792032, or approximately 9.6%.

So, the probability of winning at least once when playing the instant lottery game 5 times is approximately 9.6%.