Question

Find the probability of getting 2 or 3 tails when a coin is tossed four times.

Answer 1

Let S be the sample space associated with the experiment that a coin is tossed four times.
Then n(S) = 2⁴ = 16
Consider the following events:
A: Event of getting 2 tails
B : Event of getting 3 tails
Then A = {HHTT , HTHT, HTTH, THTH, TTHH, THHT}
n(A) = 6
$\therefore P\left(A\right)=\frac{6}{16}$
B = {HTTT, THTT, TTHT, TTTH}
n (B) = 4
$\therefore P\left(B\right)=\frac{4}{16}$
Since events A and B are mutually exclusive, we have:
$P\left(A\cap B\right)=0$
By addition theorem, we have:
P(A ∪ B) = P(A) + P (B) $-$ P (A ∩ B)
= $\frac{6}{16}+\frac{4}{16}-0=\frac{10}{16}=\frac{5}{8}$