Question

Louise has 1 white counter and 9 yellow counters in a box. louise takes one counter at random from the box, puts it back, and takes another counter from the box. a tree diagram is drawn to represent this information. find the probability that louise takes two counters of different colours.

Answer 1

The probability that Louise takes two counters of different colors is 1/5.

Step-by-step explanation:

To find the probability that Louise takes two counters of different colors, we can use a tree diagram. The first branch represents Louise taking a white counter and the second branch represents Louise taking a yellow counter. Since Louise puts the counter back before the second draw, the probabilities remain the same for both branches. The probability of taking a white counter and then a yellow counter is 1/10 (1/10 x 9/10). The probability of taking a yellow counter and then a white counter is also 1/10 (9/10 x 1/10). Adding these two probabilities together gives us 2/10, which simplifies to 1/5. Therefore, the probability that Louise takes two counters of different colors is 1/5.