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NDA Math Probability

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Question : 70 of 100

Marks: +1, -0

An unbiased coin is tossed until the first head appears or until four tosses are completed,whichever happens earlier.Which of the statements is/are correct ?

1. The probability that no head is observed is

\frac{1}{16}

2. The probability that the experiment ends with three tosses is

\frac{1}{8}

Select the correct answer using the code given below

1 only
2 only
Both 1 and 2
Neitehr 1 nor 2

Solution:

S={H,TH,TTH,TTTH,TTTT}

P(T)=P(H)=\frac{1}{2}

[Probability of getting head or tail in a single toss]

∴ Probability that no head is observed = P(TTTT)

=P(T)P(T)P(T)P(T)

=\frac{1}{2^4}=\frac{1}{16}

And the probability that the experiment ends with 3 tosses

= P (TTH)

= P(T) P(T) P(H)

=\frac{1}{8}

Hence, both statements are correct.

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