694 CHAPTER 11 Probability Example 4 uses the phrase with replacement. As in example 1, this phrase tells us that once an item is selected, it can be selected again, making it possible to select the same item twice. C S C S C S C S C S C S RMC RMS RPC RPS HMC HMS HPC HPS TMC TMS TPC TPS Sample Space Salad M Sandwich P M P M P Beverage R T H Figure 11.7 b) The tree diagram illustrating the 12 lunch specials is given in Fig. 11.7. Now try Exercise 15 c) Of the 12 lunch specials, 2 contain both a roast beef sandwich and soda (RMS, RPS). = = P(roast beef sandwich and soda are selected) 2 12 1 6 d) Of the 12 lunch specials, 3 contain neither macaroni salad nor coffee (RPS, HPS, TPS). = = P(neither macaroni salad nor coffee are selected) 3 12 1 4 7 Example 4 Selecting Balls with Replacement Two balls are to be selected with replacement from a bag that contains one red, one blue, one green, and one orange ball (see Fig. 11.8). a) Determine the number of sample points in the sample space. b) Construct a tree diagram and list the sample space. c) Determine the probability that the red ball is selected twice. d) Determine the probability that neither ball selected is orange. e) Determine the probability that the orange ball is selected at least once. Figure 11.8
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