If X = number of heads after two fair coins are tossed then, X can take the values "0,1and 2"
Since tossing the coins two times are independent from each other,
Probability of getting head or tails on first toss or second toss will be equal to "1\/2=0.5"
"1) X=0" is possible only in one case if tails comes in both the coins. So,
Possible cases: "TT"
Where T denotes tails, TT means tails on first toss and tails on second toss.
"P(X=0)= P(TT)"
where "P(TT)" means probability that Tails comes on both the coins.
"P(TT)= 0.5*0.5=0.25"
"2) X=1"
Possible cases : "HT,TH"
HT means heads on first toss and tails on second toss, TH m and tails on first toss and heads on second toss.
"P(X=1)=P(HT)+P(TH)"
"P(HT) = 0.5*0.5=0.25"
"P(TH)=0.5*0.5=0.25"
"P(X=1)=0.25+0.25=0.50"
"3) X=2"
Possible cases: "HH"
Where H denotes heads, HH means heads on first toss and heads on second toss.
"P(X=2)=P(HH)"
"P(HH)=0.5*0.5=0.25"
So, "P(X=2)=0.25"
Now, we can write the probability distribution of X as:
X P(X)
0 0.25
1 0.5
2 0.25
We can also cross check the distribution by summing all the probability, that should be equal to 1.
Comments
Leave a comment