Answer:
[tex]\frac{1}{27}[/tex]
[tex]\frac{4}{27}[/tex]
[tex]\frac{2}{27}[/tex]
[tex]\frac{1}{27}[/tex]
Explanation:
In a toss of a coin; the are two possibilities of events happening;
Either a Head or a Tail.
Given data:
Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin.
So; W = [ HHH, HHT, HTH, HTT, TTT, THT, TTH , THH]
Probability distribution of the random variable W for  a tail occurring at three coin will be
W = 3: P(3T)
= P (TTT)
= [tex](\frac{1}{3})^3[/tex]
= [tex]\frac{1}{27}[/tex]
W = 2 : P(2T, 1H)
= P( HTT, TTH, THT)
= [tex](\frac{2}{3})^2[/tex] × [tex](\frac{1}{3})[/tex]
= [tex]\frac{4}{9}*\frac{1}{3}[/tex]
= [tex]\frac{4}{27}[/tex]
W = 1 : P(1T, 2H)
= P ( HHT, HTH, THH)
= [tex](\frac{2}{3})[/tex] × [tex](\frac{1}{3})^2[/tex]
= [tex]\frac{2}{3}*\frac{1}{9}[/tex]
= [tex]\frac{2}{27}[/tex]
W = 0 : P (3H)
= P (HHH) Â
= [tex](\frac{1}{3})^3[/tex]
= [tex]\frac{1}{27}[/tex]
