Probability and Combinatorics of Letters

The video tutorial explains how to calculate the probability of typing four letters without repetition, focusing on the scenario where all four letters are vowels. It begins by determining the total number of ways to type four letters from the alphabet without repetition, using permutations. The tutorial then calculates the number of ways to type four vowels without repetition and derives the probability by dividing the two results. It also explains the probability calculation using dependent events, providing a comprehensive understanding of the concept.

What is the total number of ways to type four letters without repetition from the alphabet?

• 350,880

• 360,000

• 358,800

• 26,000

How can the number of ways to type four letters be calculated using permutations?

• By using 4 choose 26

• By using 4 permute 26

• By using 26 permute 4

• By using 26 choose 4

How many ways are there to type four vowels without repetition?

• 60

• 360

• 120

• 240

What is the probability of typing four vowels when four letters are typed without repetition?

• 0.000334

• 0.00334

• 0.0334

• 0.334

How is the probability of typing four vowels expressed as a percentage?

• 0.00334%

• 0.0334%

• 0.334%

• 3.34%

What is the probability of the first letter being a vowel?

• 5/26

• 4/25

• 3/24

• 2/23

Given the first letter is a vowel, what is the probability that the second letter is also a vowel?

• 2/23

• 5/26

• 4/25

• 3/24

If the first two letters are vowels, what is the probability that the third letter is a vowel?

• 3/24

• 2/23

• 5/26

• 4/25

What is the probability that the fourth letter is a vowel given the first three letters are vowels?

• 5/26

• 2/23

• 4/25

• 3/24

What is the product of the probabilities for each letter being a vowel?

• 120/350,880

• 120/340,000

• 120/358,800

• 120/360,000