Question

A die is thrown and a coin is tossed. What is the probabilitythat the die lands on 3 and the coin lands on heads?

Answer 1

Step-by-step explanation:

Given;

We are given a die and a coin for an experiment. The die is thrown and the coin is tossed.

Required;

We are required to find the probability that the die lands on a 3 and the the coin lands on heads.

Step-by-step solution;

To calculate the probability that the die lands on 3, we use the general formula for probabilities and that is;

Formula;

`\begin{gathered} Probability\text{ }of\text{ }an\text{ }event: \\ P[E]=\frac{Number\text{ of required outcomes}}{Number\text{ of all possible outcomes}} \end{gathered}`

Therefore, to calculate the probability of landing on a 3;

`P[3]=(1)/(6)`

Also, to calculate the probability of the coin landing on a head;

`P[heads]=(1)/(2)`

The probability of two events, that is;

`\begin{gathered} P[A]andP[B]: \\ Product\text{ }of\text{ }probabilities \end{gathered}`

Hence, the probability that the die lands on a 3 and the coin lands on a head is;

`P[3]andP[heads]=(1)/(6)*(1)/(2)`
`P[3]andP[heads]=(1)/(12)`

ANSWER:

The probability therefore is;

`(1)/(12)`