Question

A box has $4$ red, $3$ green, and $7$ blue balls. Penny picks a ball blindfolded. What is the probability of picking a blue ball or a red ball?

Answer 1

Given:

In a box,
$\bullet$ Number of red balls $=4$
$\bullet$ Number of green balls $=3$
$\bullet$ Number of blue balls $=7$

$\therefore$ Total number of balls in the box $=4+3+7=14$

Here,
$\text{P(Picking a blue ball)}=\frac{\text{Number of blue balls}}{\text{Total number of balls}}$

$\Rightarrow \text{P(Picking a blue ball)}=\frac{7}{14}$

Next,
$\text{P(Picking a red ball)}=\frac{\text{Number of red balls}}{\text{Total number of balls}}$

$\Rightarrow \text{P(Picking a red ball)}=\frac{4}{14}$

Probability that the ball picked by Penny is either blue or red, i.e., $\text{P(Picking a red or a blue ball)}$

$\text{P(Picking a blue ball or a red ball)}$
$=\text{P(Picking blue ball) + P(Picking red ball)}$

$\Rightarrow \text{P(Picking a blue ball or a red ball)}=\frac{7}{14}+\frac{4}{14}$

$\Rightarrow \text{P(Picking a blue ball or a red ball)}=\frac{7+4}{14}=\frac{11}{14}$

$\therefore$ The probability of picking a blue ball or a red ball is $\frac{11}{14}$.