Question

Two dice are thrown at the same time. Find the probability of getting.

i) both are same faces.

ii) sum of two numbers appearing an two dice is Greater than 9.

Answer 1

If the two dice are loaded…  

Let the probabilities for the first die be: a1, a2, a3, a4, a5, a6

And for the second die: b1, b2, b3, b4, b5, b6.

P(“same number”) =  

= P( { (a1, b1), (a2, b2), (a3, b3), (a4, b4), (a5, b5), (a6, b6) } )=

(since those are incompatible events)  

= P ({ (a1, b1)}) + P({ (a2, b2)}) + P({(a3, b3)}) + P( { (a4, b4)}) + P( { (a5, b5)}) + P( { (a6, b6) } )=

(since the two dice are independent)

= a1*b1 + a2*b2 + a3*b3 + a4*b4 + a5*b5 + a6*b6