Question

A coin is tossed and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing a tail and then rolling a number greater than 2. The probability of tossing a tail and then rolling a number greater than 2 is ___

Answer 1

Given that:

- A coin is tossed.

- An eight-sided dice is rolled. This is numbered 1 through 8.

1. By analyzing the information provided in the exercise, you can identify that tossing a coin and getting a tail; and rolling a dice getting a number greater than 2 are Independent Events.

2. Knowing that the probability of occurring two independent events together is equal to the product of their probabilities:

• Let be "A": Tossing a tail.

,

• Let be "B": Rolling a number greater than 2.

3. Then, the formula is:

`P(A\cap B)=P(A)\cdot P(B)`

4. You need to find:

`\begin{gathered} P(A) \\ P(B) \end{gathered}`

You can determine that:

`P(A)=(1)/(2)`

Because the coin only has two faces.

And:

`P(B)=(6)/(8)=(3)/(4)`

Because the dice has 8 sides and you need to find a number greater than 2. This gives you a set of 6 possible values:

`\lbrace3,4,5,6,7,8\rbrace`

Finally, substituting values into the formula and evaluating, you get:

`P(A\cap B)=(1)/(2)\cdot(3)/(4)=(1\cdot3)/(2\cdot4)=(3)/(8)`

Hence, the answer is:

The probability of tossing a tail and then rolling a number greater than 2 is:

`P(A\cap B)=(3)/(8)`