Example 3 A basket contains 10 red balls and 4 white balls. If three balls are taken from the basket one after the other, determine the possible values of the random variable R representing the number of red balls. Solution: Steps Solution 1. List the sample space S = (RRR, RRW. RWR, WRR, WWR, WRW, RWW, WWW} 2. Count the number of red balls in each outcome and assign this number to this outcome. Outcome Number of Red balls (Value of R) RRR 3 RRW 2 RWR 2 WRR WWR WRW RWW WWW 0 3. Conclusion The values of the random variable R (number of red balls) in this experiment are 0, 1, 2, and 3.Test I: Probability Solving Direction: Complete the table below by constructing and illustrating the probability distribution of Example 3 (refer to page 4). Steps Solution 1. List the sample space 2. Count the number of tails in each outcome and assign this number to this outcome. 3. Construct the frequency distribution of the values of the given random variable. 4. Construct the probability distribution of the given random variable by getting the probability of occurrence of each value of the random variable. 5. Construct the probability histogram.Activity I: Finding Mean: Determine the mean or expected value of each Random Variable. Write your answer in your answer sheets. 1. S 3 4 12 20 P(s) 0.1 0.5 0.2 0.2 2. 5 10 20 P(t) 50% 12% 38% 3. W 1/12 1/6 1/3 1/2 P(w) 1/2 1/10 1/5 1/5 APPLICATION Test I: Probability Solving: Find the mean, variance, and standard deviation of the following probability distribution then interpret the computed values. Write your answer in your answer sheets. 1. Variable z representing the number of male teachers per Elementary school. Z 2 3 4 5 6 P(z) 40% 32% 11% 9%% 8% 2. The number of mobile phones sold per day at a retail store varies as shown in the given probability distribution below. Find the expected number of mobile phones that will be sold in one day. X 30 33 38 40 50 P(x) 0.2 0.2 0.35 0.23 0.02