Question 14 Marks

"Eight Ball" is a game played on a pool table with $15$ balls numbered $1$ to $15$ and $a$ "cue ball" that is solid and white. Of the $15$ numbered balls, eight are solid $($non$-$white$)$ coloured and numbered $1$ to $8$ and seven are striped balls numbered $9$ to $15.$


The $15$ numbered pool balls $($no cue ball$)$ are placed in a large bowl and mixed, then one ball is drawn out at random.
Based on the above information, answer the following questions:
$(i)$ What is the probability that the drawn ball bears number $8$?
$(ii)$ What is the probability that the drawn ball bears an even number?
OR
What is the probability that the drawn ball bears a number, which is a multiple of $3$ ?
$(iii)$ What is the probability that the drawn ball is a solid coloured and bears an even number?

Answer

$(i) P ($the probability of drawing the eight ball$)$
$=\frac{\text { Number of favourable ball all to the event }}{\text { Total number of balls }}$
$=\frac{1}{15}$
$(ii)$There are $7$ even number balls $(2,4,6,8,10,12,14)$, then
$P ($the probability of drawing an even number$)$
$=\frac{\text { Number of favourable ball to the event }}{\text { Total number of balls }}$
$=\frac{7}{15}$
OR
There are $5$ balls having number multiple of $3$ , then
$P ($ the probability of drawing a multiple of three$)$
$=\frac{\text { Number of favourable balls to the event }}{\text { Total number of balls }}$
$=\frac{5}{15}=\frac{1}{5}$
$(iii)$There are $4$ balls having even number and solid, then
$P ($probability of drawing a ball with even number and solid$)$
$=\frac{4}{15}$

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