Question

There is a bag filled with 5 blue and 4 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 2 of the same colour?

Answer 1

To find the probability of drawing two marbles of the same color with replacement from a bag containing 5 blue and 4 red marbles, we calculate the probability of drawing two blue marbles and the probability of drawing two red marbles and add them together, resulting in a combined probability of 41/81.

Step-by-step explanation:

The question involves calculating the probability of drawing two marbles of the same color from a bag containing both blue and red marbles with replacement. The total number of marbles in the bag is 9 (5 blue and 4 red). Since the first marble is replaced before drawing the second one, the number of marbles in the bag remains the same for the second draw.

Here is how you calculate the probability of drawing two marbles of the same color:

• Probability of drawing two blue marbles: (5/9) for the first draw and (5/9) for the second draw, multiplied together gives (5/9) * (5/9).
• Probability of drawing two red marbles: (4/9) for the first draw and (4/9) for the second draw, multiplied together gives (4/9) * (4/9).

The total probability of drawing two marbles of the same color is the sum of the separate probabilities:

P(two blue) + P(two red) = (5/9) * (5/9) + (4/9) * (4/9).

Calculating the probabilities gives us:

P(two blue) = 25/81 and P(two red) = 16/81.

So, the combined probability is 25/81 + 16/81 = 41/81.

Answer 2

The probability is 60% that you will get the same colour twice because one colour has more marbles that the other coloured marble.