Answer:
[tex]Probability = 0.4167[/tex]
Step-by-step explanation:
Given
A toss of coin and a roll of 6-sides die
Required
P(Head and Number greater than 1)
First, we list the sample space of the coin:
[tex]Sample\ Space = \{Head, Tail\}[/tex]
From the sample space above:
[tex]P(Head) = \frac{1}{2}[/tex]
Next, we list the sample space of the die:
[tex]Sample\ Space = \{1,2,3,4,5,6\}[/tex]
There are 5 outcomes greater than 1; i.e. 2,3,4,5 and 6.
So:
[tex]P(Outcome> 1) = \frac{5}{6}[/tex]
Lastly, the required probability is calculated as:
[tex]Probability = P(Head) \ and \ P(Outcome>1)[/tex]
Change and to *
[tex]Probability = P(Head) \ * \ P(Outcome>1)[/tex]
Substitute values for P(Head) and P(Outcome > 1)
[tex]Probability = \frac{1}{2} * \frac{5}{6}[/tex]
[tex]Probability = \frac{5}{12}[/tex]
[tex]Probability = 0.4167[/tex]
