Question

Roll two (balance) dice. Let A be the event that the two numbers are the same and let B be the event that the sum of the two numbers is > 10. (i) Calculate P(A) and P(B). (ii) Are A and B independent? Calculate P(AUB).

Answer 1

Ans:- Two roll dice. Let Event A be the event that two numbers are the same and let B event be the event the sumofthe two numbers is '> (greater than or equal) to to ;. The sample spalle is (1,1),(1,2),(1,3),(1,4),(1,5),(1,6) (2,1),(2,2),(2,3), (2,4),(2,5),(2,6) (311), (3,2), (3.3), (3,4), (3,5), 6,6) (4.1), (12), (4,3), (4,4), (4-5),(436) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6) (6,1),(6:2), (6,3), (6,4),(6,5), (6,6)} A be the Event that t100 numbers are some i) A={(1,1), (2,2),(3,5)(4,4) (5,5) (66)} n(A)= li total number of our comes in Event A) .. n=36 3 6 PCA) = n(A) n 6 36 p(A) Ź B be the Event that sum of two number'sis 210 B={(4,6), (5,5), (5,6),(6,4),(6,5),(6,6)} n(B) = 6

P(B) = n(B) n 6 36 p(B) = 6 i. PCA)= 1 6 f P(B) = 6 let AMB= f (5,5), (6,6)} ie. AnB = 0 h( 0 0 9) - 2 ie. The common pool occur in event a g event B ie. PCAD 0 .. Phe event Ag event o gre independant :: PCANB) = P(A) x PCB) ol- at 6 prang) - 36 P(AUD)= P(A) + P(B) - P(ANB) et to - 1736 cost dio zlo PLAUB) .. :: PLAUB)= 36