Given:
One coin is tossed 3 times.
Required:
We need to find the probability of
a) 3 heads,
b) 3 tails and
c) tails then heads, then tails
Explanation:
The sample space for tossing a coin 3 times
[tex]S=\lbrace HHH,HTT.HTH.HHT.HTT,THH,TTT.TTH.HHT.TTT\rbrace[/tex][tex]n(S)=8[/tex]a)
Let A be the event of getting 3 heads.
[tex]A=\lbrace HHH\rbrace[/tex][tex]n(A)=1[/tex]The probability of getting three heads is
[tex]P(3\text{ heads\rparen=}\frac{n(A)}{n(S)}=\frac{1}{8}[/tex]b)
Let B be the event of getting 3 tails.
[tex]B=\lbrace TTT\rbrace[/tex][tex]n(B)=1[/tex]The probability of getting three tails is
[tex]P(3\text{ tails\rparen=}\frac{n(B)}{n(S)}=\frac{1}{8}[/tex]c)
Let C be the event of getting tails then heads, then tails
[tex]C=\lbrace THT\rbrace[/tex][tex]n(C)=1[/tex]The probability of getting tails then heads, then tails is
[tex]P(\text{ tails then heads, then tails\rparen=}\frac{n(C)}{n(S)}=\frac{1}{8}[/tex]Final answer:
[tex]P(3\text{ heads\rparen}=\frac{1}{8}[/tex][tex]P(3\text{ tails\rparen}=\frac{1}{8}[/tex][tex]P(\text{ tails then heads, then tails\rparen}=\frac{1}{8}[/tex]