Question

A bag contain 16 coins of which two are counterfeit with heads on both sides.The rest are fair coins. One is selected at random from bag and tossed. The probability of getting a head is

• A. $\frac{9}{16}$
• B. $\frac{11}{16}$
• C. $\frac{5}{9}$
• D. none of these

Answer 1

Answer: (A)

$\frac{9}{16}$

16 coins - 14 are fair and the other 2 have heads on both sides.

E1: Event that a fair coin is picked

E2; Event that a counterfeit is picked

A: Event of getting a head

So, probability of getting a head , $P\left(A\right)$

= $P\left(E1\right).P\left(\frac{A}{E1}\right)+P\left(E2\right).P\left(\frac{A}{E2}\right)=\frac{14}{16}.\frac{1}{2}+\frac{2}{16}.1=\frac{9}{16}$