Question

A bag contains several marbles: 4 red, 3 blue, 2 yellow, and 6 orange. What is the probability of choosing a red marble, replacing it, and then choosing a blue marble?

Answer 1

Given :

There are 4 red, 3 blue, 2 yellow and 6 orange marbles in a bag.

To Find :

The probability of choosing a red and then a blue marble (with replacement).

Solution :

A bag contains the number of red marbles = 4

Blue marbles = 3

Yellow marbles = 2

and orange marbles = 6

Total marbles in the bag = 4 + 3 + 2 + 6 = 15 marbles.

$Probability=\frac{\text{favorable outcome}}{\text{total outcome}}$

Probability of choosing a red marble P₁ = $\frac{4}{15}$

then replaced the red marble, so both events are independent.

the probability of choosing a blue marble P₂ =  $\frac{3}{15}$

P = P₁ × P₂

  $=\frac{4}{15}\times \frac{3}{15}$

  =   $\frac{12}{225}$

  = 0.0533 or 5.33%

The probability of choosing a red and then a blue marble is 0.0533 or 5.33%.