Question

Two dice are thrown let A be the event that the sum of the points on the faces is 9

Answer 1

If the sum of the points on the faces is 9, then A is the case.

B is the case where at least one number 6 is present.

To Find :  P(AUB)

Step-by-step explanation:

• There are two dice tossed.

• As a result, the number of alternative outcomes is 6 × 6 = 36.

• P(AUB)  =  P(A) + P (B) - P ( A∩B)

• A = sum of the points on the faces is 9.

• => A = {  ( 3 , 6) , ( 4 , 5) , ( 5 , 4  ) , ( 6 , 3) }

• => n(A) = 4

• B =   at least one number 6.

• => B = {  (1 , 6) , ( 2 ,6 ) , ( 3  , 6) , ( 4 , 6) , (  5 , 6) , ( 6 , 6) , ( 6 , 5) , ( 6 , 4) , ( 6 ,3 ) , ( 6 ,2 ) , ( 6 , 1) }

• n(B) = 11

• A∩B  means sum of the points on the faces is 9. and at least one number 6.

• =>  A∩B  =  {  ( 3 , 6)  , ( 6 , 3) }

• n ( A∩B) = 2

• n (AUB)    = 4 + 11   - 2   = 13

• P(AUB)=  = 13/36

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