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

Answer:

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 $P(A) = \frac{1}{2} = 0.5$

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 $P(B) = \frac{3}{8} = 0.375$

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