Two unbiased coins are tossed simultaneously. Find the probability of getting
$i .$ two heads
$i i .$ one tail
$i i i .$ at least one tail
$i v .$ at most one tail
$v .$ no tail

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Solution

If two unbiased coins are tossed simultaneously, then the total outcomes may be $H H, H T, T H, T T$ .
No. of total outcomes = $4$

$(i)$ two heads
favourable outcome for two heads are $H H$ .
No. of favourable outcomes = $1$
$P (two heads) = \frac{1}{4}$

$(i i)$ favourable outcome for one tail are $T H, H T$ .
No. of favourable outcomes = $2$
$P (one tail) = \frac{2}{4} = \frac{1}{2}$

$(i i i)$ favourable outcome for at least one tail are are $T H, H T, T T$ .
No. of favourable outcomes = $3$
$P (at least one tail) = \frac{3}{4}$

$(i v)$ favourable outcome for at least one head are are $T H, H T, H H$ .
No. of favourable outcomes = $3$
$P (at least one head) = \frac{3}{4}$

$(v)$ favourable outcome for no tail are $H H$ .
No. of favourable outcomes = $1$
$P (no tail) = \frac{1}{4}$

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