The probability of obtaining an odd number and a head is 1/4.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Let A be Sam rolls a fair dice.
Sample space, s = { [tex]1,2,3,4,5,6[/tex] }
⇒ [tex]n(s)=6[/tex]
An event A is obtaining an odd number, e = { [tex]1,3,5[/tex] }
⇒ [tex]n(e)=3[/tex]
The probability of A is obtaining an odd number,
[tex]P(A)=\frac{n(e)}{n(s)}[/tex]
⇒ [tex]P(A)=\frac{3}{6}[/tex]
⇒ [tex]P(A)=\frac{1}{2}[/tex]
Now, let B be Sam flips a fair coin.
Sample space, s = { [tex]H,T[/tex] }
⇒ [tex]n(s)=2[/tex]
An event B is getting a head, e = { [tex]H[/tex] }
⇒ [tex]n(e)=1[/tex]
The probability of B is getting a head,
[tex]P(B)=\frac{1}{2}[/tex]
Both A and B are independent events.
Thus the probability of obtaining an odd number and a head is
[tex]P(e)= P(A)P(B)[/tex]
⇒ [tex]P(e)=(\frac{1}{2})( \frac{1}{2} )[/tex]
⇒ [tex]P(e)=\frac{1}{4}[/tex]
Hence we can conclude that the probability of obtaining an odd number and a head is 1/4.
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