Question

You have a jar with 10 marbles. 6 marbles are red. 4 marbles are blue. You draw three marbles with replacement. What is the probability that at least one marble is red?

Answer 1

There are 10 marbles in the jar. There are 6 red marbles and 4 blue marbles.

The formula to calculate the probability of an event is given to be:

`P=\frac{\text{Number of required events }}{\text{Total number of events}}`

The probability of picking a red marble is:

`P(r)=(6)/(10)=(3)/(5)`

The probability of picking a blue marble is:

`P(b)=(4)/(10)=(2)/(5)`

To get the probability of drawing at least one red marble after 3 tries with replacement, we can find the probability of not picking a red ball at all, that is all blue, and subtract the value from 1.

The probability of picking all blue marbles can be gotten using the product of the individual probabilities, such that:

`P(3\text{ }blues)=P(b)* P(b)* P(b)`

Therefore, we have:

`P(3blues)=(2)/(5)*(2)/(5)*(2)/(5)=(8)/(125)`

Therefore, the probability that at least one marble is red is:

`P(at\text{ least one red})=1-(8)/(125)=(117)/(125)`

Therefore, the probability of picking at least one red marble is 117/125 or 0.936