A coin is tossed 4 times. Match the probability of the different outcomes given below.

\frac{15}{16}

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\frac{1}{16}

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\frac{3}{8}

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Solution

Sample space =
$⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} T T H T, T T T H, T T T T, T T H H T H H T, T H T H, T H T T, T H H H H T H T, H T T H, H T T T, H T H H H H H T, H H T H, H H T T, H H H H \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$

Total number of outcomes $= 16$
Favourable outcome for getting all heads $= {H H H H}$

Number of favourable outcomes $= 1$

Probability of getting all heads $= \frac{Number of favourable outcomes}{Total number of outcomes} = \frac{1}{16}$

P(atleast one tail) = 1 - P (heads only)
$\Rightarrow$ P(Atleast one tail) $= 1 - \frac{1}{16}$
$= \frac{15}{16}$

Favourable outcomes for 2 heads and 2 tails $= {H H T T, T T H H, T H H T, H T T H, T H T H, H T H T} = 6$

P(2 heads and 2 tails) $= \frac{6}{16}$

$= \frac{3}{8}$

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Question 4
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