
Concept explainers
To explain: The probability that password begins with a consonant.
F. 2126 H. 2136G. 2135 J. 536

Answer to Problem 89HP
The probability is 2136 . Option H. is correct.
Explanation of Solution
Given information:
A 5-character password can contain the number 0 through 9 and 26 letters of the alphabet. None of the letters is repeated.
Formula used:
Probability of an event is calculated as number of favorable outcomes divided by total number of outcomes which is mathematically expressed as,
P(E)=number of favorable outcomestotal number of outcomes
Calculation:
Consider the given information that “A 5-character password can contain the number 0 through 9 and 26 letters of the alphabet. None of the letters is repeated.”
Recall that probability of an event is calculated as number of favorable outcomes divided by total number of outcomes which is mathematically expressed as,
P(E)=number of favorable outcomestotal number of outcomes
Since, password can take 10 digits and 26 letters, the total number of outcomes is,
10+26=36
Since, the password has to begin with a consonant, number of consonants in the alphabets is 21 out of 26 .
So, favorable outcomes are 21.
Probability that password begins with consonant is,
P(E)=number of favorable outcomestotal number of outcomesP(E)=2136
Thus, the probability is 2136 . Option H. is correct.
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