Question

A coin is tossed and a die is rolled. Find the probability of getting a head and a number greater than 1.

Answer 1

Given that a coin is tossed and a die is rolled.

Let's find the probability of getting a head and a number greater than 1.

To find the probability of getting a head and a number greater than 1, apply the formula:

P(head and 1) = P(head) x P(greater than 1)

Where:

Number of heads in a coin = 1

A coin contains a head and a tail. ==> 2 possible outcomes

Numbers greater than one in a die = 2, 3, 4, 5, 6, ==> 5 numbers.

A dies contains 6 numbers ==> 6 possible outcomes

Therefore, we have:

`\begin{gathered} P(\text{head)}=(1)/(2) \\ \\ P(\text{greater than 1)=}(5)/(6) \end{gathered}`

Thus, finding the probability, we now have:

`\begin{gathered} P(\text{head and 1) = }(1)/(2)*(5)/(6)=(1*5)/(2*6)=(5)/(12) \\ \\ P(\text{head and 1) = }(5)/(12) \end{gathered}`

Therefore, the probability of getting a head and a number greater than 1 is:

`(5)/(12)`

ANSWER:

`(5)/(12)`