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)
              = \[\frac{6}{16} + \frac{4}{16} - 0 = \frac{10}{16} = \frac{5}{8}\]