Tammy is playing a game where she is trying to roll a three with a standard die if she gets a three in any of her first four rolls she wins other wise she loses what is the likelihood that Tammy wins?

To find the likelihood that Tammy wins by rolling at least one three in her first four rolls of a standard die, we can calculate the probability of losing (not rolling a three) and subtract it from 1. The probability of not rolling a three on a single roll is ( \frac{5}{6} ). Therefore, the probability of not rolling a three in four rolls is ( \left(\frac{5}{6}\right)^4 \approx 0.4823 ). Thus, the probability that Tammy wins by rolling at least one three in four rolls is ( 1 - \left(\frac{5}{6}\right)^4 \approx 0.5177 ), or about 51.77%.