Question

If two coins are tossed simultaneously, then what is the probability of getting exactly two tails?

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{4}$

$\underset{–}{\text{Given}:}$
Two coins are tossed simultaneously

$\therefore$ Total number of possible outcomes $=4$, as depicted in sample space diagram below,
$\underset{–}{\text{Need to Find}:}$
Probability of getting exactly two tails

Number of favorable outcomes
$=$ Number of exactly two tails is sample space diagram
$=1$, as can be seen in the diagram below,
$\text{P(getting exactly two tails)}=\frac{\text{Number of favorable outcomes to getting exactly two tails}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(getting exactly two tails)}=\frac{1}{4}$

$\underset{–}{\text{ALTERNATE METHOD}:}$
As given in the question, two coins are tossed samultaneously.

$\underset{–}{\text{Coin-1}:}$
Sample Sapce $=\left\{\text{H, T}\right\}$
Total number of possible outcomes $=2$

Number of favorable outcomes to getting tails $=1$

$\therefore$ Probability of tail on coin-1, $\text{P(T}{}_1)=\frac{\text{Number of favorable outcomes to getting tails}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(T}{}_1)=\frac{1}{2}$

$\underset{–}{\text{Coin-2}:}$
Sample Sapce $=\left\{\text{H, T}\right\}$
Total number of possible outcomes $=2$

Number of favorable outcomes to getting tails $=1$

$\therefore$ Probability of tail on coin-2, $\text{P(T}{}_2)=\frac{\text{Number of favorable outcomes to getting tails}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P(T}{}_2)=\frac{1}{2}$

$\underset{–}{\text{Need to Find}:}$
Probability of getting exactly two tails, i.e., probability of getting tails on both the coins, i.e., $\text{P(T}{}_1\text{and T}{}_2)$

As we know,

$\text{P(T}{}_1\text{and T}{}_2)=\text{P(T}{}_1)\times \text{P(T}{}_2)$

$\Rightarrow \text{P(T}{}_1\text{and T}{}_2)=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Hence, probability of getting exactly two tails when two coins are tossed simultaneously is $\frac{1}{4}.$

Therefore, option (a.) is the correct choice.