a bag contains all the letters in the word calculate. what is the probability of drawing a t, replacing it…

Explanation:

Step1: Count total letters

The word "CALCULATE" has 9 letters.

Step2: Calculate probability of drawing a T

There is 1 'T' in the 9 - letter word. So the probability of drawing a T, $P(T)=\frac{1}{9}$.

Step3: Calculate probability of drawing a vowel

The vowels in the English alphabet are a, e, i, o, u. In the word "CALCULATE", the vowels are 'A', 'U', 'A', 'E'. There are 4 vowels out of 9 letters. So the probability of drawing a vowel, $P(V)=\frac{4}{9}$.

Step4: Use multiplication rule for independent events

Since the first letter is replaced before the second draw, the two events are independent. The probability of both events occurring is $P = P(T)\times P(V)$. $P=\frac{1}{9}\times\frac{4}{9}=\frac{4}{81}$

Answer:

$\frac{4}{81}$