Answer
The total number of outcomes is equal to 16 $(n(S) = 16)$
The elements of the event $E$ are: $E = \{ HTTT, THTT, TTHT, TTTH, TTTT\}$
And the probability of $E$ is equal to $\frac 5 {16}$
Work Step by Step
Four coins are tossed.
1. A coin toss can result in Head or Tails, both outcomes with the same probability of occurring, so:
$S = \{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, TTHH, HTHT, THTH, THHT, HTTT, THTT, TTHT, TTTH, TTTT\}$
Therefore: $n(S) = 16$, which is the total number of outcomes.
2. The set: "E" will have all the outcomes with fewer heads then tails:
$E = \{ HTTT, THTT, TTHT, TTTH, TTTT\}$
$n(E) = 5$
3. Calculate the probability:
$P(E) = \frac{n(E)}{n(S)} = \frac 5 {16}$
