The letters C,A,R,E,S are placed in a box. Without looking Jorelle picks a letter tile from the box and records the result before placing it back. If he repeats the procedure 100 times,how many times will the letter A tile be picked?
Since Jorelle is replacing the letter tile after each pick, the probability of picking the letter A is the same for each pick.
There are 5 letters in the box, and only 1 of them is A. Therefore, the probability of picking the letter A on any one draw is:
P(A) = 1/5
So out of 100 draws, we would expect Jorelle to pick the letter A:
Expected number of A picks = (P(A)) x (total number of draws)
Expected number of A picks = (1/5) x 100
Expected number of A picks = 20
Therefore, we would expect Jorelle to pick the letter A 20 times out of 100 draws. However, since this is a probability problem, there is some variation in the actual number of A picks we might observe in 100 trials.
To determine the number of times the letter "A" tile will be picked, we need to calculate the probability of picking the letter "A" on each trial and then multiply it by the total number of trials.
Given that there are a total of 5 letters in the box (C, A, R, E, and S), and the tile is placed back into the box after each pick, the probability of picking the letter "A" on each trial is 1 out of 5 (1/5).
Therefore, the number of times the letter "A" tile will be picked can be calculated as follows:
Number of trials x Probability of picking "A" = 100 x (1/5) = 20.
Hence, the letter "A" tile will be picked 20 times in 100 trials.