Question

ou toss a pair of dice. (a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.) 36 Correct: Your answer is correct. (b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die

Answer 1

Answer:

a) The total possible outcomes are n(S) = 6² = 36

b)

The possible outcomes are possible with even numbers appearing on both dice

{ (2,2) , (2,4),(2,6), (4,2),(4,4),(4,6) ,(6,2),(6,4),(6,6) =9

The number of Exhaustive cases n(E) = 9

Step-by-step explanation:

Explanation:-

a)

when two dice are thrown

The Possible outcomes are

(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)

The total possible outcomes are n(S) = 36

b)

The possible outcomes are possible with even numbers appearing on both dice

{ (2,2) , (2,4),(2,6), (4,2),(4,4),(4,6) ,(6,2),(6,4),(6,6) =9

The number of Exhaustive cases n(E) = 9

Probability    

                    $P(E) = \frac{n(E)}{n(S)} = \frac{9}{36} = \frac{1}{4} = 0.25$