Question

selecting a letter of the alphabet if 5 letters of the alphabet are selected at random, find the probability of getting at least 1 letter y. letters can be used more than once. enter your answer as a fraction or a decimal rounded to 3 decimal places. p(at least 1 letter y) =

Explanation:

Step1: Find the probability of getting no 'y's

There are 26 letters in the alphabet. The probability of not getting a 'y' in one - selection is $\frac{25}{26}$. Since the selections are independent and we are making 5 selections, the probability of getting no 'y's in 5 selections is $(\frac{25}{26})^5$.
$(\frac{25}{26})^5=\frac{25^5}{26^5}=\frac{9765625}{11881376}\approx0.822$

Step2: Find the probability of getting at least 1 'y'

The probability of getting at least 1 'y' is the complement of the probability of getting no 'y's. Let $P(X\geq1)$ be the probability of getting at least 1 'y' and $P(X = 0)$ be the probability of getting no 'y's. Then $P(X\geq1)=1 - P(X = 0)$.
$P(X\geq1)=1-(\frac{25}{26})^5=1 - \frac{9765625}{11881376}=\frac{11881376 - 9765625}{11881376}=\frac{2115751}{11881376}\approx0.178$

Answer:

$\frac{2115751}{11881376}\approx0.178$