Question

8. (20 points) A letter ofRandom word REMEMBER. FindProbability caught: a. Letter R b.Letter E c. Letter R or M d. Letter R or E*

Answer 1

Given the word REMEMBER, we want to know the probability of getting the following letter by picking one at random from the word.

item (a):

The probability of getting a letter is given by the ratio between the amount of the desired letter by the total of letters. Since we want the letter R, the probability of getting R is the amount of R's(2), by the total amount of letters(8).

$\frac{2}{8}=\frac{1}{4}=0.25$

The probability of getting R is 25%.

item (b):

Now we want the letter E. We just need to use the same process as we did in the previous item.

$\frac{3}{8}=0.375$

The probability of getting an E is 37.5%.

item (c):

The probability of getting either R or M, is given by the sum of the probabilities of getting R or M. From the first item we already know that p(R) = 0.25. Let's calculate

$p(M)=\frac{2}{8}=\frac{1}{4}=0.25$

Now, we just sum those probabilites.

$p(RorM)^{}=p(R)+p(M)=0.25+0.25=0.5$

The probability of getting R or M is 50%.

item (d):

$p(RorE)=p(R)+p(E)=0.25+0.375=0.625$

The probability of getting R or E is 62.5%.

.