Aspire Faculty ID #17546 · Topic: UGC NET Computer Science August 2024 (Paper II) · Just now
UGC NET Computer Science August 2024 (Paper II)

A coin is tossed successively three times. Find the Probability $(P)$, Event $(E)$, Sample space $(S)$ of getting exactly one head or two heads, where $n$ is number of occurrence.

(A) $n(S)=8$ and $n(E)=4$

(B) $n(E)=6$ and $n(S)=8$

(C) $P(E)=\frac{3}{4}$

(D) $P(E)=\frac{1}{2}$

Choose the correct answer from the options given below :

Solution

Sample space for 3 tosses:

$S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}$

Thus

$n(S)=8$

Event: exactly 1 head or 2 heads

1 head → ${HTT,THT,TTH}$

2 heads → ${HHT,HTH,THH}$

So

$n(E)=6$

Probability

$P(E)=\frac{6}{8}=\frac{3}{4}$

Thus correct statements:

(B) and (C)

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