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An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each $(a, b, c, d)$ with one option being the correct answer. The other 2 questions have two options each, namely true and false. A candidate randomly ticks the options. Then, the probability that he/she will tick the correct option in atleast four questions, is
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Verified Answer
The correct answer is:
$\frac{3}{64}$
Total sample space, $n(S)=4^{3} \cdot 2^{2}$ and total number of favourable cases
$$
n(E)=\left({ }^{3} C_{1} \cdot 3+{ }^{2} C_{1} \cdot 1\right)+1
$$
$\therefore$ Required probability $=\frac{n(E)}{n(S)}$
$$
=\frac{{ }^{3} \mathrm{C} \cdot 3+{ }^{2} \mathrm{C}_{1} \cdot 1+1}{4^{3} \cdot 2^{2}}=\frac{3 \cdot 3+2+1}{4^{3} \cdot 4}
$$
$=\frac{12}{64 \cdot 4}=\frac{3}{64}$
$$
n(E)=\left({ }^{3} C_{1} \cdot 3+{ }^{2} C_{1} \cdot 1\right)+1
$$
$\therefore$ Required probability $=\frac{n(E)}{n(S)}$
$$
=\frac{{ }^{3} \mathrm{C} \cdot 3+{ }^{2} \mathrm{C}_{1} \cdot 1+1}{4^{3} \cdot 2^{2}}=\frac{3 \cdot 3+2+1}{4^{3} \cdot 4}
$$
$=\frac{12}{64 \cdot 4}=\frac{3}{64}$
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