An instant lottery game gives you probability 0.023 of winning on any one play. Plays are independent of each other.
If you play 2 times, the probability that you win on one or more of your plays is about? (±0.0001)
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For either-or probabilities, you add the individual probabilities.
.023 + .023 = ?
For winning on both/all you multiply the probabilities.
.023 * .023 = ?
The first answer is for winning on either one of the plays, while the second is for winning on both ("or more"). From the information I have given you, can you combine the two answers?
To find the probability that you win on one or more of your plays when playing 2 times, you can use the concept of complementary probability.
The complementary probability is the probability that the event of interest does not happen. In this case, the complementary event is not winning on any of the plays.
Since the plays are independent, the probability of not winning on any one play is given by (1 - 0.023) = 0.977 (approximately).
To find the probability of not winning on any of the plays, we raise this probability to the power of the number of plays. So, the probability of not winning on any of the two plays is 0.977^2 = 0.9553 (approximately).
Finally, to find the probability of winning on one or more plays, we subtract the probability of not winning on any of the plays from 1. So, the probability of winning on one or more plays when playing 2 times is approximately 1 - 0.9553 = 0.0447 (approximately).
Therefore, the probability that you win on one or more of your plays when playing 2 times is about 0.0447 (±0.0001).