Question

What is the probability that in three throws of a dice, one gets exactly two 6s?

• A. \( \frac{1}{18} \)
• B. \( \frac{5}{72} \)
• C. \( \frac{1}{12} \)
• D. \( \frac{7}{72} \)
• E. \( \frac{1}{24} \)

Hint:

For probability questions involving multiple dice or throws, first identify the favorable outcomes and then calculate the total number of possible outcomes.

Answer 1

The Correct Option is B

Step 1: Identifying the favorable outcomes.
To get exactly two 6s, the possible outcomes are as follows: \[ \text{(6, 6, other)}, \text{ (6, other, 6)}, \text{ (other, 6, 6)} \] In each case, the third die will show any number other than 6, which can be \( 1, 2, 3, 4, \) or \( 5 \). So, there are 5 possible outcomes for the third die.
Step 2: Counting the total outcomes.
The total number of outcomes for three dice is: \[ 6 \times 6 \times 6 = 216 \] Step 3: Calculating the probability.
The favorable outcomes for exactly two 6s are 5. Therefore, the probability is: \[ \frac{5}{216} \] Final Answer: \[ \boxed{\frac{5}{72}} \]