Question

Roll a 6-sided die and a 10-sided die. (Both dice are fair and have an ace side.)

What is the chance that they will both land on ace?  (Give exact answer.)

What is the chance that neither will land on ace?  (Give exact answer.)

What is the chance that at least one will not land on ace?  (Give exact answer.)

Answer 1

P( 6 sided die will land on ace ) = 1/6

P( 10-sided die will land on ace ) = 1/10

a) P( Both will land on ace) = P( 6 sided die will land on ace ) *P( 10-sided die will land on ace )

= ( 1/6) * (1/10)

= (1/60)

b) P( Neither will land on Ace) = P( 6 sided die will not land on ace )* P( 10-sided die will not land on ace )

= [ 1- (1/6)] * [ 1- (1/10)]

= (5/6) * (9/10)

= 45/ 60

= 3/4 = 0.75

c) P( Atleast one will land on ace) = 1- P( Non will land on ace)

= 1- (3/4) \

= 1/4 = 0.25