Respuesta :
SOLUTION
(33) The question says a coin is tossed and a die with 6 faces is rolled, what is the probability of getting a head and a 3.
Probability is given as
[tex]Probability=\frac{expected\text{ outcome}}{total\text{ outcome }}[/tex]Now, a coin has two faces, a head and a tail. So, total outcome is 2 faces.
We want to get the probability of getting a head. This becomes
[tex]\begin{gathered} Probability\text{ of head = }\frac{expected\text{ outcome}}{total\text{ outcome}}=\frac{1\text{ head}}{2\text{ faces}} \\ =\frac{1}{2} \\ P(head)=\frac{1}{2} \end{gathered}[/tex]So, probability of getting a head is 1/2
A die has 6 faces labelled 1, 2, 3, 4, 5 and 6
Probability of getting a 3 should be
[tex]\begin{gathered} Probability\text{ of getting 3 = }\frac{one\text{ face showing 3}}{6\text{ faces}} \\ that\text{ is }\frac{1}{6} \end{gathered}[/tex]So, probability of getting a 3 is 1/6
Now probability of getting a head and a 3, that is P(head and 3), means we multiply both probabilities, we have
[tex]\begin{gathered} P(head\text{ and 3\rparen = }\frac{1}{2}\times\frac{1}{6} \\ =\frac{1}{12} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{12}[/tex]