Question

A pair of dice is rolled. What is the probability that the sum of the numbers on the dice is 8 given that neither of the dice shows the number 3?

Answer 1

Hi there!
Here's the answer:

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¶ Probability of Occurrence of Event

$P(E) = \frac{No.\: of\: Favourable\: Outcomes}{No.\: of\: Total\: Outcomes}$

¶ Total Outcomes when ' n ' dice are rolled = $6^{n}$

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SOLUTION:

Let S be the sample space
n(S) - No. of Total Outcomes when 2 dice are rolled
n(S) = 6² = 36

Let E be the Event that Sum of No.s on both the dice is 8 and 3 shouldn't be shown on any of the two.

E = { (1,7) , (2,6) , (4,4) , (6,2) , (7,1)}

n(E) is the No. of favourable cases for occurrence of Event E, which is equal to No. of cases in set E
n(E) = 5

Probability $P(E) = \frac{n(E)}{n(S)}$

=> $P(E) = \frac{5}{36}$

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$\underline{\underline{Required\: Probability =\frac{5}{36}}}$

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Hope it helps