Question

A coin is tossed an eight sided die numbered 1 through 8 is rolled find the probability of tossing a head and then rolling a number greater than 6. Round to three decimal places if needed

Answer 1

We are given that a coin is tossed and a die numbered from 1 through 8 is rolled. To determine the probability of tossing head and then rolling a number greater than 6 is given by the following formula:

`P(\text{head and n>6)=p(head)}\cdot p(n>6)`

This is because we are trying to determine the probability of two independent events. The probability of getting heads is given by:

`P(\text{heads})=(1)/(2)`

This is because there are two possible outcomes, heads or tails and we are interested in one of the outcomes.

Now we determine the probability of getting a number greater than 6 when rolling the dice. For this, there are 8 possible outcomes and we are interested in two of them, these are the numbers greater than 6 on the die (7, 8). Therefore, the probability is:

`P(n>6)=(2)/(8)=(1)/(4)`

Now we determine the product of both probabilities:

`P(\text{head and n>6)=}(1)/(2)*(1)/(4)=(1)/(8)`

Now we rewrite the answer as a decimal:

`P(\text{head and n>6)=}0.125`

Therefore, the probability is 0.125.