Question

Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed (a) What is the probability that the numbers add up to 9? (b) What is the probability that the sum of the numbers is less than 5? (a) The probability that the sum of the numbers is 9 is (Type an integer or a simplified fraction)

Answer 1

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Answer 2

SOLUTION ;

a.

We may get sum of 9 of numbers on the face upward of red and green die,

In the following outcomes)

(Red, green) : (3, 6), (6,3), (4,5), (5,4) 

P(3, 6) = P(6,3) = P(4, 5) = P(5, 4) = 1/6 * 1/6 = 1/36

P( sum =  9) 

= P(3, 6) + P(6,3) + P(4, 5) + P(5, 4) 

= 1/36 + 1/36 + 1/36 + 1/36

= 4/36

= 1/9 

So, probability that the sum of numbers is 9 = 1/9 (ANSWER).

b.

P(sum < 5)

Following possible outcomes are there to get sum < 5 :

(1, 1), (1, 2), (2, 1), (2, 2), (3, 1) , (1, 3) 

Each outcome has probability = 1/6 * 1/6 = 1/36

So, P( sum < 5) 

= 6 outcomes * P(each outcome)

= 6 * 1/36

= 1/6

So, probability that the sum of numbers is less than 5 = 1/6 (ANSWER).