An instant lottery scratch-off game offers a 0.04 probability of winning on any one play. Plays are independent of each other. If you play 7 times, what is the probability you win at least once?
That equals 1 minus the probability of never winning on any of 7 plays.
1 - (0.96)^7 = 24.9%
To solve this problem, we can use the concept of complementary probability. The complementary probability of an event A is defined as 1 minus the probability of A occurring. In this case, the event A is winning at least once.
The probability of winning on any one play is given as 0.04, and the plays are independent of each other. Therefore, the probability of not winning on any one play is 1 minus the probability of winning, which is 1 - 0.04 = 0.96.
Now, to find the probability of not winning in all 7 plays, since the plays are independent, we can multiply the probability of not winning on each play together. So, the probability of not winning in all 7 plays is 0.96^7.
Finally, we can use the concept of complementary probability to find the probability of winning at least once. The complementary probability of not winning at least once is the probability of winning none of the 7 times.
Therefore, the probability of winning at least once = 1 - the probability of winning none of the 7 times = 1 - 0.96^7.
Calculating this, we find that the probability of winning at least once in 7 plays is approximately 0.266, or 26.6%.