Probability- Math problem

Question

The letters for each of the following words are placed in two separate bags. The letter with the highest probability of being chosen out of its bag is the first letter of the suspects name. Remember: Simplify fraction, if necessary.

Junk

P(J) = _____

Exaggerate

P(G) =____ Suspects name starts with: __

How do I solve this? (This is clue 1 and problem 1 of a murder worksheet I am doing)

Answer 1

In the word "Junk", each letter appears only once, and there are four letters total. This means that each of the four letters has a 1 in 4 chance of being picked from the bag.

P(J) = 1/4

P(u) = 1/4

P(n) = 1/4

P(k) = 1/4

In the word "Exaggerate" there are 10 letters total, but some of the letters happen more than once. For example, three of the 10 letters in the bag are "e"s. If we are looking for the probability of selecting a "g" out of the bag, we need to look at how many "g"s there are total in the word (2) out of how many total letters (10). This means there is a 2 in 10 chance that a g will be picked.

P(g) = 2/10 = 1/5 (simplified)

Then, we need to compare our two probabilities to determine which letter has a higher probability of being selected.

P(J) = 1/4 = 0.25 = 25% (1 divided by 4 = 0.25, 0.25 x 100 = 25%)

P(g) = 1/5 = 0.2 = 20% (1 divided by 5 = 0.2, 0.2 x 100 = 20%)

The probability of pulling a "j" out of bag #1 is 25%, while the probability of pulling a "g" out of bag #2 is 20%. 25% is a higher probability than 20%, so P(J) is the more likely option.