Question

a box contains 20 marbles, 12 red and 8 blue. What is the probability for picking a blue marble and after replacing it picking a red marble​

Answer 1

`(6)/(25)`

Explanation:

Probability of an event can be formed from the fraction where the numerator is the number of desired outcomes and the denominator is the number of total outcomes. In this case, there are 20 marbles, so 20 total outcomes. The desired outcome is first picking a blue, replacing it, and then picking a red. Since you are replacing the marble, these events are independent, which means that they don't rely on previous events and the probability of picking a red or blue is the same each time:

`(blue)/(marbles)=(8)/(20)=(2)/(5)`

`(red)/(marbles)=(12)/(20)=(3)/(5)`

When we combine independent events, we multiply the probabilities:

`(2)/(5)*(3)/(5)=(6)/(25)`