Question 12 Marks
An experiment consists of rolling a die until a $2$ appears:
How many elements of the sample space correspond to the event that the $2$ appears on the $k^{th}$ roll of the die?
$[$Hint: First $(k - 1)$ rolls have $5$ outcomes each and $k^{th}$ rolls should result in $1$ outcomes$]$
How many elements of the sample space correspond to the event that the $2$ appears on the $k^{th}$ roll of the die?
$[$Hint: First $(k - 1)$ rolls have $5$ outcomes each and $k^{th}$ rolls should result in $1$ outcomes$]$
Answer
View full question & answer→Number of outcomes when die is thrown is $‘6\ ’$.
If $2$ appears on the $A^{th}$ roll of the die.
So$,$ first $(k - 1$) roll have $5$ outcomes each and $K^{th} $roll results $2$
Number of outcomes $= 5^{k-1}$
If $2$ appears on the $A^{th}$ roll of the die.
So$,$ first $(k - 1$) roll have $5$ outcomes each and $K^{th} $roll results $2$
Number of outcomes $= 5^{k-1}$