What is the probability of selecting a woman as the first participant in this study? o Step 1: Find the sample space. The sample space consists of a population of 432 people; the sample space is 432. o Step 2: Find f(x). The outcome, x, is the number of women who can be selected from this population. There are 212 women; f(x) = 212. Thus, the probability of selecting a woman as the first participant is p = .49: P (selecting a woman) = 212/432 = .49 Ex 2: Miltenberger and colleagues (2003) conducted a study on compulsive buying. As part of their study, they asked participants whether they felt satisfaction or relief when engaging in compulsive shopping. Of the 19 participants who completed their survey, 5 said only satisfaction, 3 said only relief, and 11 said both. What is the probability that participants in this study felt only satisfaction, only relief, or both from compulsive buying? o Step 1: Find the sample space. In this study, Miltenberger and colleagues (2003) observed 19 participants; the sample space is 19. o Step 2: Find f(x). We know that 5 participants felt satisfaction, f(x) = 5; 3 felt relief, f(x) = 3; and 11 felt both, f(x) = 11. Therefore, the probabilities for each response can be stated as follows: P (only satisfaction) = 5/19 = .26 P (only relief) = 3/19 = .16 P (both) = 11/19 = .58 For a given event, the relative frequency of an outcome is the probability of its occurrence. the relative frequency of an event is the probability of its occurrence. Both probability and relative frequency vary between 0 and 1 and can never be negative. To find the relative frequency and therefore the probability of an outcome, we follow two steps: o (1) distribute the frequencies and o (2) distribute the relative frequencies. Step 1: Distribute the frequencies . Table 5.1 shows how we could distribute the frequency of a coin flip. Table 5.2 shows how we could distribute the frequency of selecting men from a population consisting of 4 men and 6 women. Notice that the sum of the frequencies equals the sample space. So, by distributing frequencies in Step 1, you can find the sample space, which is the denominator of the probability formula. Sides of a coin F(x) Heads 1 Tails 1 Sample space = 2
Sex F(x) Men 4 Women 6 Sample space = 10 The relative frequency of an outcome is the probability of observing that outcome. Step 2: Distribute the relative frequencies . Table 5.3 shows how we could dis-tribute the relative frequency of a coin flip. Table 5.4 shows how we could distribute the relative frequency of selecting a man from a population consisting of 4 men and 6 women. In both examples, the relative frequency is the probability of observing each outcome. Sides of a coin F(x) P(x) Heads 1 .50 Tails 1 .50 Sample space = 2 ∑p(x)= 1.00 Sex F(X) P(X) MEN 4 .40 Women 6 .60 Sample space= 10 ∑p(x)=1.00 Ex 3: Dai, Wertenbroch, and Brendl (2008) showed participants 57 pictures of flowers and 57 pictures of birds on a computer screen. Participants, not being told how many pictures of each were shown, were then asked to estimate how many pictures of flowers and birds were shown.