Question

Watson flips two fair coins, and in agreement with his friend Smith to give him $\$20$ if both the coins land on tails. What is the probability (in percent) that Smith will get $\$20$?

• A. 25

Answer 1

The correct option is A 25
Let's see what happens when Smith tosses two fair coins.
Suppose, heads= $\text{H}$ and tails= $\text{T}$

$\underset{–}{\text{Tossing coin 1:}}$

Sample space= $\text{{H, T}}$
Total number of possible outcomes= $2$
Favorable outcome to land tails up= {T}
Number of favorable outcome= $1$

$\text{P(T)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(T)}=\frac{1}{2}$

$\underset{–}{\text{Tossing coin 2:}}$
Similar to coin 1, probability of tails up when 2nd coin is flipped, $\text{P(T)}=\frac{1}{2}$

The probability of getting $2$ tails when two coins are tossed:

$\text{P(T and T) = P(T)}\times \text{P(T)}$

$\Rightarrow \text{P(T and T)}=\frac{1}{2}\times \frac{1}{2}$
$\Rightarrow \text{P(T and T)}=\frac{1}{4}=0.25$
$\Rightarrow \text{P(T and T) in percent}=0.25\times 100=25\%$

$\underset{–}{\text{Alternate Method:}}$

Total possible outcomes: $\text{{HH, HT, TH, TT}}$.

Out of $4$ possibilities, only $1$ signifies tails on both the coins which is $\text{TT}$.

Therefore, the probability of getting tails on both the coins is $\frac{1}{4}=0.25=25\%.$


$\therefore$ Watson's friend Smith has $25\%$ chance of getting $\$20$ for landing tails on both the coins.