Question

Event A: the coin lands on heads
Event B: the die is 3 or greater
P(A and B)=

Answer 1

Since the events are independent,
`P(A\cap B)=P(A)\cdot P(B)`.

`A` - the coin lands on heads

`|\Omega|=2\\|A|=1\\\\P(A)=(1)/(2)`

`B` - the die is 3 or greater

`|\Omega|=6\\|B|=4\\\\P(B)=(4)/(6)=(2)/(3)`

Therefore

`P(A\cap B)=(1)/(2)\cdot(2)/(3)=(1)/(3)`