MATH SOLVE

2 months ago

Q:
# A pair of dice consisting of a six-sided die and a four-sided die is rolled and the sum is determined. Let A be the event that a sum of 5 is rolled and let B be the event that a sum of 5 or a sum of 9 is rolled. Find(a)P(A),(b)P(B), and (c) P(A \ B)

Accepted Solution

A:

Answer:P(A) = 1 / 6P(B) = 1 / 4P(A\B) = 0Step-by-step explanation:It is given that the a six-sided die and a four-sided die is rolledThus,the total number of outcome = 6 Γ 4 = 24A = event that a sum of 5 is rolledB = event that a sum of 5 or a sum of 9Now,a) For P(A)The possible outcomes for event A = (1,4), (2,3), (3,2), (4,1) Thus, the total number of possible outcomes for the given event = 4therefore, P(A) = 4 / 24 orP(A) = 1 / 6b) For P(B) The possible outcomes for event B = (5,4), (6,3) and possible outcomes for event Athus, the total number of possible outcomes for the given event = 2 + 4 = 6therefore,P(B) = 6 / 24orP(B) = 1 / 4c) P(A\B)Since, it is impossible to get both the sum of 5 and sum of number = 9, Hence, the P(A\B) = 0