Question

Two dice (one red and one blue) are thrown. Find the probability that the sum is prime and the number on the red die is greater than the blue die.

Hint:

In probability problems with multiple conditions, list outcomes carefully to avoid missing or extra cases.

Answer 1

Step 1: Find total possible outcomes.
When two dice are thrown, total outcomes:
\[ 6 \times 6 = 36 \]
Step 2: Identify prime sums.
Possible prime sums are:
\[ 2,\;3,\;5,\;7,\;11 \]
Step 3: List favorable outcomes with red die>blue die.
Valid outcomes satisfying both conditions are:
\[ (2,1),\ (3,2),\ (4,1),\ (4,3),\ (5,2),\ (6,1) \]
Step 4: Count favorable outcomes.
Number of favorable outcomes = 6
Step 5: Calculate probability.
\[ \text{Probability} = \frac{6}{36} = \frac{1}{6} \]
Step 6: Conclusion.
The required probability is \(\boxed{\dfrac{1}{6}}\).