Note 1. Rolling a fair die does not influence the outcomes of tossing a fair coin 2. Neither tossing a fair coin affects the outcomes of rolling a fair die 3. Both events do not affect each other so they are independent events
Probability =
Number of possible selection
Number of samples
P(A∩B)=P(A)×P(B) Thus you calculate the probability of each event separately and multiply them to get the independent probability Samples for coin ={ Head, Tail } Number of samples for coin =2 Number of tail(s) = 1 P( Tail )=
1
2
Samples for die ={1,2,3,4,5,6} Number of samples for die =6 Odd numbers are numbers not divisible by 2 . Thus there is a remainder when divided by 2. Odd numbers from the die samples are {1,3,5} Number of odd numbers =3 P(Odd)=
3
6
=
1
2
Note: 3 divides itself 1 time and 6, 2 times P(Tail and Odd) =P( Tail )×P( Odd ) P(Tail and Odd) =