Exercise 1 Page 939

We want to find the probability that Alana will spell the word MATH correctly. To do it, we will use the theoretical probability. P=Favorable Outcomes/Possible Outcomes We will start by finding the number of possible outcomes, which is the number of permutations of the letter tiles she has in the bag. Let's recall the formula for the number of permutations of n objects. _nP_n=n! Since there are 4 tiles, in our case n=4. Therefore, the number of possible outcomes is 4!. Let's evaluate it. 4! = 4 * 3 * 2 * 1 = 24 Next we will look for the number of favorable outcomes. There is only one way in which Alana can select a permutation that spells the word MATH correctly. Therefore, there is only 1 favorable outcome. This means that we have enough information to calculate the desired probability. P=Favorable Outcomes/Possible Outcomes [0.9em] ⇕ P=1/24 This corresponds to answer D.