Q.2.19 - A First Course in Probability

Question

Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow, and the other

painted white. When this pair of dice are rolled, what is the probability that both dice land with the same color face up?

Step-by-Step Solution

Answer

The probability that both dice land with the same color face-up is$0.28$.

Step 1 Given Information.

Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow, and the other painted white.

Step 2 Explanation.

The same color on face-up can be any of the $4$colors. Let's find the probability of landing a color when only $1$dice are rolled.

$\begin{array}{rcl}\mathrm{P}\left(\text{ red }\right)& =& 2/6\mathrm{P}\left(\text{ black }\right)\\ & =& 2/6\mathrm{P}\left(\text{ white }\right)\\ & =& 1/6\mathrm{P}\left(\text{ yellow }\right)\\ & =& 1/6\end{array}$

Since both dice are independent of each other we can just multiply the individual values to get probabilities for the same color on the up face.

$$\begin{gathered} P(red )=(2 / 6) *(2 / 6)=4 / 36 \\ P( black )=(2 / 6) *(2 / 6)=4 / 36 \\ P(white )=(1 / 6) *(1 / 6)= 1 / 36 \\ P(yellow )=(1 / 6) *(1 / 6)=1 / 36 \end{gathered}$$

$\text{P(same color)=P(red )+P(black )+P(white )+P(yellow)}$

$\begin{array}{rcl}P(Same colour)& =& (4 / 36)+(4 / 36)+(1 / 36)+(1 / 36)\\ & =& 10 / 36\\ & =& 0.28\end{array}$