Question

A coin is tossed. If the results in a head, a coin is tossed, otherwise a die is thrown. Describe the following events:
$A=$getting at least one head, $B=$ getting an even number, $C=$ getting a tail, $D=$getting a tail and an odd number.

Answer 1

Step 1: Find the sample space if the tossing of the coin results in head, a coin is tossed, otherwise a die is thrown:

When the first coin is head, then again a coin is tossed.

Then the sample space will be $S=\{HH,HT,TH,TT\}$

Let $S_1$ be the number of events when the throw results in head i.e., $\left\{H\right\}$, then a coin will be tossed again,

Thus, the possible outcomes will be $\{HH,HT\}$.

Let $S_2$ be the number of events when the throw results in tail i.e., $\left\{T\right\}$, then a die will be thrown,

Thus, the sample space will be,

$S_2=\{(T1),(T2),(T3),(T4),(T5),(T6\left)\right\}$

Step 2: Find the event of getting at least one head:

The possible outcomes of getting at least one head will be,

$A=\{HH,HT\}$

Step 3: Find the event of getting an even number:

The possible outcomes of getting an even number will be,

$B=\{T2,T4,T6\}$

Step 4: Find the event of getting a tail:

The possible outcomes of getting a tail will be,

$C=\{T1,T2,T3,T4,T5,T6,HT\}$

Step 5: Find the event of getting a tail and an odd number:

The possible outcomes of getting a tail and an odd number will be,

$D=\{T1,T3,T5\}$

Final answer:

Hence, the event of

$A=$getting at least one head

$A=\{HH,HT\}$

$B=$ getting an even number

$B=\{T2,T4,T6\}$

$C=$ getting a tail

$C=\{T1,T2,T3,T4,T5,T6,HT\}$

$D=$getting a tail and an odd number.

$D=\{T1,T3,T5\}$