1. Roll a pair of fair dice. (A) what is the probability that the sum of the num
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1. Roll a pair of fair dice. (A) what is the probability that the sum of the numbers is 7 or 11? (B) what is th probability that both dice either turn up the same number or that the sum of the numbers is less than 5? 1. Roll a pair of fair dice. (A) what is the probability that the sum of the numbers is 7 or 11? (B) what is th probability that both dice either turn up the same number or that the sum of the numbers is less than 5? (A) what is the probability that the sum of the numbers is 7 or 11? (B) what is th probability that both dice either turn up the same number or that the sum of the numbers is less than 5?Explanation / Answer
When rolling 2 dice, the total outcomes = 62 = 36
Probability = Favourable outcomes/Total outcomes
(A) P(Sum is 7 or 11) = P(Sum = 7) + P(Sum = 11)
P(Sum = 7) ---- (1+6), (6+1), (2+5), (5+2), (3+4), (4+3) = 6 outcomes
P(Sum = 11) ----- (5+6), (6+5) = 2 outcomes
Therefore Favourable outcomes = 6 + 2 = 8
The Required Probability = 8/36 = 2/9
(B) P(Both Turn up same or the Sum is < 5) = P(Both Turn up same) + P(Sum = 2) + P(Sum = 3) + P(Sum = 4)
P(Both Turn up same) = (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6 outcomes
P(Sum =2) = (1+1). But this outcome has been counted in P(Both turn the same). Therefore 0 outcomes.
P(Sum = 3) = (1+2), (2+1) = 2 outcomes.
P(Sum = 4) = (1+3), (3+1) and (2+2), but (2+2) has been already counted in P(Both same), therefore only 2 outcomes here are counted.
Total Favourable outcomes = 6 + 0 + 2 + 2 = 10
The Required Probability = 10/36 = 5/18
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