Question

ASSIGNMENTSCOURSESAssignment 5. Conditional ProbabilityAct 1 of 3SECTION 2014Two 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 3Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blepoza10NEXT QUESTIONASK FOR HELPTURNI

Answer 1

The total number for the sample space for two cubes rolled is 36

1,1; 1,2....; 1,6

2,1; 2,2..; 2,6

. .

. .

6,1; 6,2...; 6,6

Event A (less than 10; 1 - 9)

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

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

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

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

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

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

The sample space has 30 elements

$Pr\text{ (<10) = }\frac{30}{36}\text{ = }\frac{5}{6}$

P (A) = 0.83

Event B (sum of numbers on both cubes is a multiple of 3)

Event A already happened, we have Event B as:

(1,2); (1,5)

(2,1); (2,4)

(3,3); (3,6)

(4,2); (4,5)

(5,1); (5,4)

(6,3)

The sample space has 11 elements

$Pr\text{ (multiple of 3) = }\frac{11}{30}\text{ = 0.367}$

P (B|A) = 0.37