Two number cubes are rolled for two separate events: Event A is the event that the sum of numbers on both cubes is less than 10.

Event B is the event that the sum of numbers on both cubes is a multiple of 3.

Complete the conditional probability formula for event B given that event A occurs first by writing A and B in the blanks:

P ( _a0 | _a1) = P ( _a2 ∩ _ a3)

P ( _a4)

Step-by-step explanation:

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

          (2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

          (3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

                    (4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

                              (5, 4), (5, 3), (5, 2), (5, 1)

                                        (6, 3), (6, 2), (6, 1)

       = 30

P(B) = (1, 2), (2, 1)                                   sum = 3

          (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)    sum = 6

          (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)  sum = 9

          (6, 6)                                           sum = 12

      = 12

P(A ∩ B) =  (1, 2), (2, 1)

                  (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

                  (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

             = 11

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb