Face 1 2 3 4 5 6 Frequency 12 18 \(y\) 30 \(2y\) 45 Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining ...

Answer Details

The table shows the frequency of each face when a fair die is tossed 150 times. To find the probability of obtaining a 5, we need to look at the frequency of the face with the value 5, which is given as 2y. We are not given the value of y, but we know that the die is fair, which means that each face has an equal probability of appearing on any given toss. Since there are six faces on a die, the probability of obtaining a 5 on any given toss is 1/6. Therefore, the probability of obtaining a 5 in this experiment is the frequency of the face with value 5 (2y) divided by the total number of tosses (150), multiplied by the probability of obtaining a 5 on any given toss (1/6): P(5) = (2y/150) x (1/6) = y/225 We don't know the value of y, but we can simplify the expression by noting that the probabilities of all six faces must add up to 1: P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1 We can substitute the expressions for the probabilities in terms of y and simplify: 12/150 + 18/150 + y/150 + 30/150 + 2y/150 + 45/150 = 1 105/150 + 3y/150 = 1 3y/150 = 45/150 y = 15 Substituting y = 15 into the expression for P(5), we get: P(5) = 15/225 = 1/15 Therefore, the probability of obtaining a 5 is 1/15, which corresponds to option C.