Q. 2.19 - A First Course in Probability

Question

Two symmetric dice have had two of their sides painted red, two sides painted black, one painted yellow and the other painted white. When this pair of dice rolled, what is the probability that both dice land with same color face up$?$

Step-by-Step Solution

Answer

The probability that both dice land with the same color is \( \frac{5}{18} \approx 0.2778 \).

Step 1: Identify the probabilities for each color

Each die has 6 faces: 2 red, 2 black, 1 yellow, 1 white.
\( P(\text{Red}) = 2/6 = 1/3 \), \( P(\text{Black}) = 2/6 = 1/3 \), \( P(\text{Yellow}) = 1/6 \), \( P(\text{White}) = 1/6 \).

Step 2: Compute probability of same color

\( P(\text{same}) = P(R)^2 + P(B)^2 + P(Y)^2 + P(W)^2 = (1/3)^2 + (1/3)^2 + (1/6)^2 + (1/6)^2 \)
\( = 1/9 + 1/9 + 1/36 + 1/36 = 4/36 + 4/36 + 1/36 + 1/36 = 10/36 = 5/18 \approx 0.2778 \).