Final answer:
To find the probability of picking four vowels out of seven tiles picked at random, use combinations to calculate the number of ways to choose the vowels and consonants. Then divide by the total number of ways to choose seven tiles.
Step-by-step explanation:
To find the probability that four out of seven tiles picked at random are vowels, we need to find the number of ways to choose four vowels out of the 44 available vowels, and then multiply it by the number of ways to choose the remaining three consonants out of the 56 available consonants. This can be calculated using combinations.
The group of interest is the group of four vowels, which has a size of 4. The sample size is the total number of tiles picked, which is 7.
The probability is given by: P(4 vowels) = (number of ways to choose 4 vowels out of 44) * (number of ways to choose 3 consonants out of 56) / (number of ways to choose 7 tiles out of 100).