Respuesta :
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;
[tex]\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}[/tex]Therefore, to calculate the probability of landing on a 3;
[tex]P[3]=\frac{1}{6}[/tex]Also, to calculate the probability of the coin landing on a head;
[tex]P[heads]=\frac{1}{2}[/tex]The probability of two events, that is;
[tex]\begin{gathered} P[A]andP[B]: \\ Product\text{ }of\text{ }probabilities \end{gathered}[/tex]Hence, the probability that the die lands on a 3 and the coin lands on a head is;
[tex]P[3]andP[heads]=\frac{1}{6}\times\frac{1}{2}[/tex][tex]P[3]andP[heads]=\frac{1}{12}[/tex]ANSWER:
The probability therefore is;
[tex]\frac{1}{12}[/tex]