Question

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 5. The probability of tossing a tail and then rolling a number greater than 5 is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

The probability of tossing a tail and then rolling a number greater than 5 is 0.1875 (or 18.75%).

Step-by-step explanation:

To find the probability of tossing a tail and then rolling a number greater than 5, we need to first consider the individual probabilities of each event.

The probability of tossing a tail with a fair coin is 0.5 (or 1/2).

The probability of rolling a number greater than 5 with an eight-sided die is 3/8, since there are three numbers (6, 7, and 8) that are greater than 5 out of a total of eight possible outcomes.

To find the probability of both events happening, we multiply the probabilities of each event together:

P(Tail and Number > 5) = P(Tail) * P(Number > 5) = 0.5 * 3/8 = 0.1875

Therefore, the probability of tossing a tail and then rolling a number greater than 5 is 0.1875 (or 18.75%).

Answer 2

The probability of tossing a tail and then rolling a number greater than 5 is 0.188

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, we have that:

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

In this question:

The coin and the die are independent. So

Event A: Tossing a tail.

Event B: Rolling a number greater than 5.

Probability of tossing a tail:

Coin can be heads or tails(2 outcomes), so the probability of a tail is
`P(A) = (1)/(2) = 0.5`

Probability of rolling a number greater than 5:

8 numbers(1 through 8), 3 of which(6,7,8) are greater than 5. So the probability of rolling a number greater than 5 is
`P(B) = (3)/(8) = 0.375`

Probability of A and B:

`P(A \cap B) = P(A)*P(B) = 0.5*0.375 = 0.188`

The probability of tossing a tail and then rolling a number greater than 5 is 0.188