What is the probability of a disaster occurring?

Question

You have 11 cards (2 - 12) and 2 dice (6-sided) you draw 3 cards randomly and roll the dice. What is the probability of the sum of the 2 dice equaling any one of the three cards causing a disaster?

Answer 1

Let the sum of the 2 dice equals k. The value k could be from 2 to 12.

What is the probability that anyone of the 3 selected cards equals k?

Consider the complement event: all three selected cards are different from k.

P(all three selected cards are different from k) = ₁₀C₃ / ₁₁C₃ = 8/11

So, P(anyone of the 3 selected cards equals k) = 1 - 8/11 = 3/11.

This probability is the same for any value of k,

so P(a disaster occurring) = 3/11.