Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 285. Approximate the probability that at least 75 rolls are needed to get this sum. Probability

1

Step-by-step explanation:

Probability is given by number of possible outcomes : number of total outcomes

Assuming we stop rolling the six-sided die once our sum is 290 (exceeds 285)

Number of possible outcomes = 75, number of total outcomes = 290

Probability (75 rolls are needed to get this sum) = 75/290 = 0.259

Probability (more than 75 rolls are needed to get this sum) = 1 - 0.259 = 0.741

Probability (at least 75 rolls are needed to get this sum) means that either 75 rolls or more than 75 rolls are needed to get this sum = 0.259 + 0.741 = 1