grace rolls a fair, 6 - sided die 50 times. what is the probability that she rolls at least one 6? round…

Explanation:

Step1: Find probability of not rolling a 6 on one roll

The probability of not rolling a 6 on a single roll of a 6 - sided die is $P(\text{not }6)=\frac{5}{6}$.

Step2: Find probability of not rolling a 6 in 50 rolls

Since the rolls are independent events, the probability of not rolling a 6 in 50 rolls is $(\frac{5}{6})^{50}$.

Step3: Find probability of rolling at least one 6

The probability of rolling at least one 6 is the complement of the probability of not rolling a 6 in 50 rolls. So $P(X\geq1)=1 - P(X = 0)=1-(\frac{5}{6})^{50}$. Calculate $(\frac{5}{6})^{50}\approx0.000128$. Then $1-(\frac{5}{6})^{50}\approx1 - 0.000128=0.999872\approx0.9999$.

Answer:

0.9999