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?
To determine the probability of getting at least 1 red marble, we need to consider the possible outcomes.
The total number of marbles in the bag is 4 blue + 5 red = 9 marbles.
First, let's consider the probability of not getting any red marbles on the first draw. Since there are 5 red marbles out of 9 marbles in total, the probability of not getting a red marble on the first draw would be 5/9.
Next, for the second draw, we also need to consider the probability of not getting a red marble. However, since the marble is replaced after each draw, the probabilities for each draw are independent. So, the probability of not getting a red marble on the second draw would also be 5/9.
The probability of not getting any red marbles on both draws is calculated by multiplying the probabilities for each draw: (5/9) * (5/9) = 25/81.
To find the probability of getting at least 1 red marble, we need to subtract the probability of not getting any red marbles from 1 (since the sum of all possible outcomes must equal 1). Therefore, the probability of getting at least 1 red marble is 1 - 25/81 = 56/81.
So, the probability of getting at least 1 red marble is 56/81.
"at least 1 red" also means "not 2 blue"
p(not blue) = 5 / (4 + 5) = 5/9
p(at least 1 red) = 1 - (5/9)^2