Question

In the game of Scrabble, each player begins by drawing 7 tiles from a bag initially containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Suppose you are playing Scrabble and get to go first. If you randomly select 7 tiles from the bag, what’s the probability that all of them are vowels? Use combinations to help answer this question.

Answer 1

The probability of drawing 7 vowels from a bag of 100 tiles in Scrabble is approximately 0.0037.

Step-by-step explanation:

To calculate the probability that all 7 tiles drawn are vowels, we need to find the ratio of the number of favorable outcomes to the total number of possible outcomes.

There are 42 vowels and 100 total tiles in the bag. We can use combinations to calculate the number of ways to choose 7 vowels from 42. The formula for combinations is: nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects being chosen.

Using this formula, the number of ways to choose 7 vowels from 42 is:

42C7 = 42! / (7!(42-7)!) = (42*41*40*39*38*37*36) / (7*6*5*4*3*2*1) = 600,766,320

The total number of ways to choose 7 tiles from 100 is:

100C7 = 100! / (7!(100-7)!) = 160,075,608

Therefore, the probability of drawing 7 vowels from the bag is:

P(7 vowels) = 600,766,320 / 160,075,608 ≈ 0.0037 (rounded to four decimal places)