UPSC NDA 2 2019 Mathematics Solved Paper

Concept:
If A,B and C are 3 independent events, then P(A∩B∩C)=P(A)×P(B)×P(C)
Calculation:
Given coin is biased heads comes up thrice as likely as tails.
⇒P(H)=‌

3

4

‌ and ‌P(T)=‌

1

4

Let, T be a random variable for the no. of tails for 3 independent tosses.
⇒P(T=0)=P(HHH)=(‌

3

4

)3=‌

27

64

⇒P(T=1)=P(HHT,THH,HTH)=3×(‌

3

4

×‌

3

4

×‌

1

4

)=‌

27

64

⇒P(T=2)=P(TTH,THT,HTT)=3×(‌

1

4

×‌

1

4

×‌

3

4

)=‌

9

64

⇒P(T≤2)=P(T=0)+P(T=1)+P(T=2)=‌

27

64

+‌

27

64

+‌

9

64

=‌

63

64

=0.98