Question

Four coins are tossed together. The probability that head will appear on at least one of the four is $3k/16$.Find the value of $k$

Answer 1

Probability that head appears on atleast one of the coins$=1-$Probability that there is no heads$=1-P\left(\overline{H_1}\overline{H_2}\overline{H_3}\overline{H_4}\right)=1-P\left(\overline{H_1}\right)P\left(\overline{H_2}\right)P\left(\overline{H_3}\right)P\left(\overline{H_4}\right)=1-\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)=\frac{15}{16}=\frac{3k}{16}\Rightarrow k=5$