<p>A biased coin such that the probability of obtaining a tail is 0.7. The biased coin is being tossed 5 times. Find the probability that
</p>
<ol class="i-list"><li><div class="list-item-paragraph">exactly 3 tails are obtained,</div></li><li><div class="list-item-paragraph">less than 2 tails are obtained,</div></li><li><div class="list-item-paragraph">at least 2 tails are obtained.</div></li></ol>

A biased coin such that the probability of obtaining a tail is 0.7. The biased coin is being tossed 5 times. Find the probability that


Default solution

Let \(X\) be the number of tails obtained out of 5 tosses.

\[P(3 \text{ tails}, 2 \text{ heads}) = (0.7)^3 \times (0.3)^2 \times \frac{5!}{3!2!}\]

Required Prob \(= P(0 \text{ tail}) + P(1 \text{ tail}, 4 \text{ heads})\)

\[= 0.3^5 + 0.3 \times 0.7^4 \times \frac{5!}{1!4!}\]

\[= 0.7^0 \times 0.3^5 \times {}^5C_0 + 0.7^1 \times 0.3^4 \times {}^5C_1\]

\[P(\text{at least 2 tails}) = P(2 \text{ tails}) + P(3 \text{ tails}) + \ldots\]

Worked Example 1

Worked Example 1

Video Solution:

Default solution