Question

Eight ordinary fair dice are rolled. What is the probability that at least two of these dice will land with the number 6 showing?

A) (5/6)⁸+(8/1) (1/6) (5/6)⁷
B) 1 - (5/6)⁸ (1/6) (5/6)⁷
C) (8/2) (1/6)² (5/6)⁶
D) (5/6)⁸ + (1/6) (5/6)⁷
E) 1 - (5/6)⁷ - (1/6) (5/6)⁷

Answer 1

The probability that at least two dice will land with the number 6 showing is 1 - (5/6)^8.

Step-by-step explanation:

The probability that at least two dice will land with the number 6 showing can be found by subtracting the probability that no dice land with 6 showing from 1. To find the probability that no dice show 6, we need to find the probability that each die shows a number other than 6. This probability is (5/6) for each die. Since there are 8 dice, the probability that no dice show 6 is (5/6)^8. Therefore, the probability that at least two dice show 6 is 1 - (5/6)^8.

Option B) correctly represents this probability as 1 - (5/6)^8 (1/6) (5/6)^7.