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

Answer:

1. $\frac{1}{4}$
2. $\frac{1}{8}$

Step-by-step 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, $|A|=\left\{H\right\},\ so\ P(A)=\dfrac{1}{2}$

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

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

$P(A\ and\ B)=P(A)\cdot P(B)=\dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{4}$

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, $|C|=\left\{T\right\},\ so\ P(C)=\dfrac{1}{2}$

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

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

$P(C\ and\ D)=P(C)\cdot P(D)=\dfrac{1}{2}\cdot \dfrac{1}{4}=\dfrac{1}{8}$

Answer 2

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.