The probability that Luca will win Wheel of Letters for this considered case is 6/13
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For this case, the sample space of result of wheel of letters spin is
S = {A, B, ..., Z} , thus, n(S) = size of S = 26
Let E = event that the spinner will stop in one of the letters in “COUNTRY PHRASE”
Then, the outcomes in favor of E are {'P', 'O', 'C', 'A', 'T', 'R', 'Y', 'N', 'H', 'S', 'U', 'E'}
Thus, n(Favorable cases for E) = 12 (counted unique ones, and not repeated), as each letter is only 1 time in the spinner.
Thus, we get:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{12}{26} =\dfrac{6}{13}[/tex]
Thus, the probability that Luca will win Wheel of Letters for this considered case is 6/13
Learn more about probability here:
brainly.com/question/1210781
