Probability Question 6

Mr. Schulte has a fair 12-sided die, with the sides numbered from 1 through 12. On both Monday and Tuesday, Mr. Schulte will roll the die 1 time. If the side that lands faceup is numbered with a prime number, Mr. Schulte will collect the homework that day—otherwise, he will not collect the homework. What is the probability that Mr. Schulte will collect homework on both Monday and Tuesday?

(Note: 1 is NOT a prime number.)

\left(\dfrac{5}{12}\right)^2

\left(\dfrac{6}{12}\right)^2

\left(\dfrac{7}{12}\right)^2

2\left(\dfrac{5}{12}\right)

2\left(\dfrac{6}{12}\right)

Approach

The prime numbers are 2, 3, 5, 7, 11

Therefore, the probability of collecting homework each day is:

P(\text{collect homework}) = \frac{5}{11}

The probability that homework will be collected both days:

P(\text{collect homework on Monday}) \cdot P(\text{collect homework on Tuesday})

= \frac{5}{12}\cdot \frac{5}{12} = \boxed{\left(\frac{5}{12}\right)^2}