An instant lottery gives you probability of 0.023 of winning on any one play, which are independent of each other. If you play 6 times, the probability that you win on none of your plays is:
The answer is suppose to be .8902, but I got 0.895. I took 0.23 to the 6th power and subtracted it from 1. What am I doing wrong?
actually their answer is wrong as well
you want the prob of losing 6 times in a row, so
if prob of winning is .023 then the prob of losing in a game is .977
so prob of losing 6 consecutive times
= (.977)^6 = .8696958
To find the probability of not winning on any of your plays, you need to calculate the probability of losing on each play and then multiply them together.
First, let's calculate the probability of losing on one play. Since the probability of winning on one play is 0.023, the probability of losing on one play is 1 - 0.023 = 0.977.
Now, to find the probability of losing on all 6 plays, we multiply the probability of losing on each play together:
0.977 * 0.977 * 0.977 * 0.977 * 0.977 * 0.977 = 0.897
So, the correct probability of winning on none of your 6 plays is 0.897, not 0.895 as you calculated. It seems like there might have been a rounding error in your calculation, resulting in a slightly different value.