The soccer team's shirts have arrived in a big box and people start grabbing them. The box contains 7 medium, 12 Large, and 11 extra-large shirts.
What is the probability that the first 4 shirts are all extra large?
I have been struggling with the problem for an hour and can't seem to figure out the answer...
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
First shirt = category/total = 11/30
Second shirt, since one XL shirt is gone = 10/29
Third shirt, since two XL are gone = 9/28
Fourth shirt = ?
11/30 * 10/29 * 9/28 * ? = ?
To find the probability of drawing 4 extra-large shirts in a row from the box, we need to know the total number of shirts and the number of extra-large shirts available.
In this case, we have a total of 7 medium shirts, 12 large shirts, and 11 extra-large shirts, which makes a total of 7 + 12 + 11 = 30 shirts.
Now, to calculate the probability of drawing 4 extra-large shirts in a row, we need to consider the following steps:
Step 1: Find the probability of picking an extra-large shirt on the first draw.
There are 11 extra-large shirts out of a total of 30 shirts, so the probability of picking an extra-large shirt on the first draw is 11/30.
Step 2: Find the probability of picking an extra-large shirt on the second draw.
After removing one extra-large shirt from the box, there are now 10 extra-large shirts remaining out of 29 shirts. So the probability of picking an extra-large shirt on the second draw is 10/29.
Step 3: Continue this process for the third and fourth draws.
Step 4: Multiply the probabilities from each step together to find the probability of all four shirts being extra large.
Let's calculate:
Probability of picking an extra-large shirt on the first draw = 11/30
Probability of picking an extra-large shirt on the second draw = 10/29
Probability of picking an extra-large shirt on the third draw = 9/28
Probability of picking an extra-large shirt on the fourth draw = 8/27
To find the overall probability, we multiply these probabilities together:
(11/30) * (10/29) * (9/28) * (8/27) ≈ 0.0199
Therefore, the probability of drawing all 4 extra-large shirts in a row from the box is approximately 0.0199 or 1.99%.