Answer to Question #178225 in Statistics and Probability for Edwin

Question

Two dice are tossed. Find the probability of getting ‘an even number on the first dice or a 

total of 8 ‘.

Answer 1

If Events A and B are independent, the probability that Event A OR Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur:

P(A or B)=P(A)+P(B)−P(A and B)

The probability of getting an even number at the first die is $\frac{1}{2}$ (as the probability of even = the probability of odd $= \frac{1}{2}$ )

The probability of getting a total of 8 is $\frac{5}{6^2}$ , as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4).

The probability of getting an even number at the first die AND a total of 8 is $\frac{3}{6^2}$

The probability of getting an even number at the first die OR a total of 8 is

$= \frac{1}{2}+\frac{5}{36}-\frac{3}{36}= \frac{20}{36}$