Question

An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round your answer to four decimal places. P (Lands heads at least once) -

Answer 1

Here we have,

$P(H)=0.4$

where H denotes the event of a head showing up.

$P(atleast \hspace{.1cm}one \hspace{.1cm}Head \hspace{.1cm}in \hspace{.1cm}7 \hspace{.1cm}tosses)=1-P(no \hspace{.1cm}head \hspace{.1cm}in \hspace{.1cm}7 \hspace{.1cm}tosses)$

P(no head in 7 tosses) = P(all coins shows tails) = 0.6*0.6*0.6*.0.6 * 0.6 * 0.6 * 0.6

Hence,

$P(no \hspace{.1cm}head \hspace{.1cm}in \hspace{.1cm}7 \hspace{.1cm}tosses)=0.6^7=0.0279$

Hence,

P(Lands head at least once) = 1 - 0.0279 = 0.9720

The answer is obtained when if we consider this a random variable X where X follows a binomial distribution with parameters n = 7 and p = 0.4, were probability of success which is a head showing up.