A bag contains 5 red and 4 green apples. Michael takes one apple at random from the bag. His sister Ashley then takes an apple at random from he bag. What is the probability that the two apples are the same colour?
Can you explain to me how to do this please? Do I need a probability tree or?
A lot of wording just to confuse you. The fact that 2 people draw the apples has nothing to do with it, might just as well have Michael draw 2 apples,
assuming the first apple is not returned to the bag.
What is the prob they are both red or green ?
prob(both red) = (5/9)(4/8) = 5/18
prob(both green) = (4/9)(3/8) = 1/6
so prob(same colour) = 5/18 + 1/6 = 4/9
To find the probability that the two apples are the same color, you can use the concept of conditional probability. Here's how you can approach this problem:
1. Determine the total number of possible outcomes: In this case, the total number of possible outcomes is the total number of apples in the bag, which is 5 (red) + 4 (green) = 9 apples.
2. Determine the number of favorable outcomes: We need to consider two cases separately:
a) If Michael takes a red apple, then Ashley needs to also take a red apple. There are 5 red apples in the bag, so the favorable outcomes for this case are 5 red apples.
b) If Michael takes a green apple, then Ashley needs to also take a green apple. There are 4 green apples in the bag, so the favorable outcomes for this case are 4 green apples.
3. Calculate the probability: The probability of the two apples being the same color is the total number of favorable outcomes divided by the total number of possible outcomes.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
For our case:
Total number of possible outcomes = 9 (as calculated earlier)
Number of favorable outcomes = 5 (red + red) + 4 (green + green) = 9
Probability = 9 / 9 = 1
Therefore, the probability that the two apples are the same color is 1 or 100%.
You don't necessarily need a probability tree for this question since it only involves a single event (taking an apple out of the bag) and the probabilities are independent for each case. But a probability tree can be helpful in visualizing the different possibilities and calculating probabilities when dealing with more complex scenarios.