Question

A pair of dice are rolled​ 1,000 times with the following frequencies of​ outcomes:

Sum	2	3	4	5	6	7	8	9	10	11	12
Frequency	10	30	50	70	110	150	170	140	120	80	70

Use these frequencies to calculate the approximate empirical probabilities and odds for the events a. The sum is less than

5

or greater than

8.

b. The sum is even or exactly divisible by

3.

Answer 1

(a) sum is less than 5 or greater than 8 sum less than 5 is P(g) + P(3) + P(4) = 10 + 30+50 = 90 1000 1000 sum greater than 8 is Plaap 104 pl p/12) - 140+120780770 1000 410 1000 sum is less than 5 of greater than ses 90 +410 - 500 5 0.5 1000 1000 1000 10 = h

(o sum is even on exactly divisible by 3. d DLA = Sum is even =) p (2) + P(4)+ P(6)+ P(8)+ P(10) + P(92) 10+50+11ot 170+ 120+20 530 1000 1000 A - divisible by3 =) P(3) +P[6)+P (9) +P(12) = 30+110+140+70/1000 = 350/1000 P(AUB) z P(A) + P(B) -PLADB) P(B) =

sum TO is even and exactly divisible by 3, au 120.26 P(12) = 10 + 110 1000 1000 Sum is even of exactly divisible by 3 y 930 + 350 - 100 1000 1000 .: 1000 530 + 350 -180 1000 to 880190 - 1000 - 050 600 1000