Question

Find the probability of getting.
Atmost three heads when $4$ coins are tossed.

Answer 1

Each coin has two possible outcomes - heads or tails.

Therefore, the total number of possible outcomes is:

$2\times 2\times 2\times 2=16$ possible outcomes.

At-most three heads possibilities :

0 heads - $TTTT$- $1possibility$

1 head - $TTTH,TTHT,THTT,HTTT$ - $4possibilities$

2 heads - $HHTT,HTHT,HTTH,THHT,THTH,TTHH,$ - $6possibilities$

3 heads - $HHHT,HHTH,HTHH,THHH$ - $4possibilities$

$\therefore$Total at-most three heads possibilities $=1+4+6+4=14$

$Probability=\frac{PossibleOutcomes}{TotalOutcomes}=\frac{15}{16}$