Question continuation
Determine the following probabilities:
a. P(A)
b. P(B)
c. P(A ∩ B)
d. P(A ∪ B)
Answer:
a. P(A) = 0.1389
b. P(B) = 0.1389
c. P(AnB) = 0.0193
d. P(AuB) = 0.2585
Explanation:
Given
Password length = 6
Letters (a-z) = 26
Integers (0-9) = 10
Total usable characters = 26 + 10 = 36
a. P(A) = Probability that a password begins with vowel (a,e,i,o,u)
Probability = Number of required outcomes/ Number of possible outcomes
Number of required outcomes = Number of vowels = 5
Number of possible outcomes = Total usable characters = 36
P(A) = 5/36
P(A) = 0.13888888888
P(A) = 0.1389
b. P(B) = Probability that the password ends with an even number (0,2,4,6,8)
Probability = Number of required outcomes/ Number of possible outcomes
Number of required outcomes = Number of even numbers = 5
Number of possible outcomes = Total usable characters = 36
P(B) = 5/36
P(B) = 0.13888888888
P(B) = 0.1389
c. P(AnB)
This means that the probability that a password starts with a vowel and ends with an even number
P(AnB) = P(A) and P(B)
P(AnB) = P(A) * P(B)
P(AnB) = 5/36 * 5/36
P(AnB) = 25/1296
P(AnB) = 0.01929012345
P(AnB) = 0.0193 ----_---- Approximately
d. P(AuB)
This means that the probability that a password either starts with a vowel or ends with an even number
P(AuB) = P(A) or P(B)
P(AuB) = P(A) + P(B) - P(AnB)
P(AuB) = 5/36 + 5/36 - 25/1296
P(AuB) = 335/1296
P(AuB) = 0.25848765432
P(AuB) = 0.2585 ----_---- Approximately
