Question

Mrs. Giavis has 26 marbles in a bag. She has 13 blue marbles, 10 red marbles, and 3 yellow marbles. What is the probably that Mrs. Giavis will pick a blue marble, not replace it, and then randomly pick a red marble?

Answer 1

Given:

Total number of marbles = 26

Number of blue marbles = 13

Number of red marbles = 10

Number of yellow marbles = 3

To find:

The probability of getting a blue marble then a red marble (without replacement).

Solution:

Total number of marbles = 26

Number of blue marbles = 13

Probability of getting a blue marble is first draw is:

$P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}$

$P(Blue)=\dfrac{13}{26}$

$P(Blue)=\dfrac{1}{2}$

After drawing 1 marble, the remaining number of marbles in the bag is 25.

Probability of getting a red marble is second draw is:

$P(Red)=\dfrac{\text{Number of red marbles}}{\text{Remaining number of marbles}}$

$P(Red)=\dfrac{10}{25}$

$P(Red)=\dfrac{2}{5}$

Now the probability of getting a blue marble then a red marble (without replacement) is:

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

$P(\text{Blue then red})=\dfrac{1}{2}\times \dfrac{2}{5}$

$P(\text{Blue then red})=\dfrac{1}{5}$

Therefore, the probability of getting a blue marble then a red marble (without replacement) is $\dfrac{1}{5}$.