Question

A bag of marbles contains 3 red marbles, 7 blue marbles, and 5 orange marbles. If a marble is drawn from the bag and not replaced, then a second marble is drawn. Calculate P(red then orange):

Answer 1

Answer:

$\dfrac{1}{14}$.

Step-by-step explanation:

It is given that,

Red marbles = 3

Blue marbles = 7

Orange marbles = 5

Total marbles = 3+7+5 = 15

Probability of getting a red marble is

$P(Red)=\dfrac{\text{Red marbles}}{\text{Total marbles}}$

$P(Red)=\dfrac{3}{15}$

$P(Red)=\dfrac{1}{5}$

If a marble is drawn from the bag and not replaced. So remaining marbles is 15-1=14. Now,

Probability of getting an orange marble is

$P(orange )=\dfrac{\text{Orange marbles}}{\text{Total remaining marbles}}$

$P(orange)=\dfrac{5}{14}$

Now,

$P(\text{red then orange})=P(Red)\times P(orange)$

$P(\text{red then orange})=\dfrac{1}{5}\times \dfrac{5}{14}$

$P(\text{red then orange})=\dfrac{1}{14}$

Therefore, the required probability is  $\dfrac{1}{14}$.