Question

A six sided die is rolled and a coin is tossed. Find Plodd and T).11/121/41/2

Answer 1

You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:

`P(O\cap T)`

Where

"O" represents the event " rolling an odd number"

"T" represents the event "tossing a coin and obtaining tail"

The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:

`P(O\cap T)=P(O)\cdot P(T)`

So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)

-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:

`\begin{gathered} P(N\text{)}=\frac{\text{favorable outcomes}}{total} \\ P(N)=(1)/(6) \end{gathered}`

The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}

Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:

`\begin{gathered} P(O)=\frac{\text{favorable outcomes}}{total} \\ P(O)=(3)/(6)=(1)/(2) \end{gathered}`

So, the probability of rolling an odd number is P(O)=1/2

-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.

For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:

`\begin{gathered} P(T)=\frac{\text{favorable outcomes}}{total} \\ P(T)=(1)/(2) \end{gathered}`

The probability of tossing a coin and obtaining a tail is P(T)=1/2

Once calculated the individual probabilities you can determine the asked probability:

`P(O\cap T)=P(O)\cdot P(T)=(1)/(2)\cdot(1)/(2)=(1)/(4)`