Question

Oscar simultaneously tosses a fair coin and rolls an eight-sided fair die. The probability that Oscar gets heads and an even number is __. The probability that Oscar gets tails and a prime number less than 4 is __.

Answer 1

The number of outcomes in the experiment that Oscar did is 2 x 8  which is equal to 16. To get head is 1 and to get even number is 4. That is 4/16. Thus, the first probability being asked for 1/4. Then getting a tail is 1 and prime number less than 4 are only 2. Thus, the answer is 2/16 or 1/8. 

Answer 2

1. 
   `(1)/(4)`
2. 
   `(1)/(8)`

Explanation:

Oscar simultaneously tosses a fair coin and rolls an eight-sided fair die.

Let us assume, A be the event of getting a head and B be the event of getting an even number.

So,
`|A|=\left\{H\right\},\ so\ P(A)=(1)/(2)`

And
`|B|=\left\{2,4,6,8\right\},\ so\ P(B)=(4)/(8)=(1)/(2)`

The probability that Oscar gets heads and an even number is,

`P(A\ and\ B)=P(A)\cdot P(B)=(1)/(2)\cdot (1)/(2)=(1)/(4)`

Let us assume, C be the event of getting a tail and D be the event of getting a prime number less than 4.

So,
`|C|=\left\{T\right\},\ so\ P(C)=(1)/(2)`

And
`|D|=\left\{2,3\right\},\ so\ P(D)=(2)/(8)=(1)/(4)`

The probability that Oscar gets heads and an even number is,

`P(C\ and\ D)=P(C)\cdot P(D)=(1)/(2)\cdot (1)/(4)=(1)/(8)`