An office has $60\%$ of its area for common seating, $25\%$ of the area for cabins and rest of the area for Pantry.
Then the area used by Pantry is
$\%$ of the total office area
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Step-by-sA coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
Answer
Let the probability of getting a tail in the biased coin be x.
∴P(T)=x
⇒P(H)=3x
For a biased coin, P(T)+P(H)=1
⇒x+3x=1
⇒4x=1
⇒x=
4
1
∴P(T)=
4
1
and P(H)=
4
3
When the coin is tossed twice, the sample space is {HH,TT,HT,TH}.
Let X be the random variable representing the number of tails.
∴P(X=0)=P(notail)=P(H)×P(H)=
4
3
×
4
3
=
16
9
P(X=1)=P(onetail)=P(HT)+P(TH)
=
4
3
⋅
4
1
+
4
1
⋅
4
3
=
16
3
+
16
3
=
8
3
P(X=2)=P(twotails)=P(TT)=
4
1
×
4
1
=
16
1
tep explanation:
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