Question

Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing A: { A 3 appears on each of two dice.} Use 4 significant decimal places for your answer, and use the proper rules of rounding. I am looking for just the answer, not the equation.

Answer 1

Answer: 0.0278

Step-by-step explanation:

On a fair dice , there are six numbers (1,2,3,4,5,6) written on each face of dice.

Thus, when we thrown two dice , the sample space for the possibilities of outcomes will become :

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

i.e. Total number of outcomes = 36

For event A: { 3 appears on each of two dice.}

The favorable outcome = (3,3)

Now, the required probability : $P(A)=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$

$=\dfrac{1}{36}=0.0277777777778\approx0.0278$

Hence, the required probability is 0.0278.