NDA 2019
Exam NDA
Year 2019
Subject Mathematics
Chapter Probability NDA 2019 · Mathematics · Probability
A coin is biased so that heads comes up thrice as likely as tails....
A coin is biased so that heads comes up thrice as likely as tails. For three independent losses of a coin, what is the probability of getting at most two tails?
Options A 0.16 B 0.48 C 0.58 D 0.98
Step-by-step solution
If P ( Tails ) = x ∴ P ( Head ) = 3 x ∵ P ( T ) + P ( H ) = 1 ⇒ x = 1 4 \begin{array}{ll} & \text{ If } P(\text{ Tails })=x \\ \therefore & P(\text{ Head })=3 x \\ \because & P(T)+P(H)=1 \\ \Rightarrow & x=\frac{1}{4}\end{array} ∴ ∵ ⇒ If P ( Tails ) = x P ( Head ) = 3 x P ( T ) + P ( H ) = 1 x = 4 1 Probability of
a t m o s t 2 t a i l s at most 2 tails a t m os t 2 t ai l s = 1 − P ( all tail ) = 1 − 1 4 × 1 4 × 1 4 = 63 64 = . 98 \begin{aligned}& =1-P(\text{ all tail })\\
& =1-\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}=\frac{63}{64}\\
& =.98
\end{aligned} = 1 − P ( all tail ) = 1 − 4 1 × 4 1 × 4 1 = 64 63 = .98 $
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