Question

Two coins are tossed simultaneously. Find the probability of getting two heads, at least one head, no head.

Answer 1

Step 1: Find the sample space for tossing a coin twice:

Sample space for throwing a coin twice,

$$\begin{gathered} n\left(S\right)={\text{(number of possible outcomes of tossing a coin)}}^{\text{number of coins tossed}} \\ n\left(S\right)={\left(2\right)}^2 \\ n\left(S\right)=4 \end{gathered}$$

Thus, the sample space of tossing a coin twice will be,

$S_1=\{HH,HT,TH,TT\}$

Step 2: Find the probability of getting two heads:

From the sample space, the favourable outcomes of getting two heads are $\left\{HH\right\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$\text{Probability=}\frac{1}{4}$

Therefore, the probability of getting two heads will be $\frac{1}{4}$.

Step 3: Find the probability of getting at least one head:

From the sample space, the favourable outcomes of getting at least one head are $\{HH,HT,TH\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$\text{Probability=}\frac{3}{4}$

Therefore, the probability of getting at least one head will be $\frac{3}{4}$.

Step 4: Find the probability of getting no head:

From the sample space, the favourable outcomes of getting no head are $\left\{TT\right\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$\text{Probability=}\frac{1}{4}$

Therefore, the probability of getting no head will be $\frac{1}{4}$.

Final answer:

Hence, the Probability of getting two heads will be $\frac{1}{4}$, at least one head will be $\frac{3}{4}$, no head will be $\frac{1}{4}$.