Question

There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting at least 1 red?

Answer 1

Answer:

$\dfrac{65}{81}$ or 80.25%

Step-by-step explanation:

Number of blue Marbles = 4

Number of Red Marbles = 5

Total Number of marbles =4+5=9

$P(B)=\dfrac49\\\\P(R)=\dfrac59$

In the experiment, two marbles are chosen one after the other with replacement.

The possible outcomes are: BB, BR, RB and RR

The probability of getting at least 1 red

=P(BR or RB or RR)

=P(BR)+P(RB)+P(RR)

$=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}$

Expressed as a percentage, we have:

$\dfrac{65}{81}\times100=80.25\%$

The probability of getting at least 1 red is 80.25%.