1. isabel briggs myers was a pioneer in the study of personality types. the personality types are broadly defined according to four main preferences. do married couples choose similar or different personality types in their mates? the following data give an indication. similarities and differences in a random sample of 375 married couplesnumber of similar preferences number of married couplesall fourthreetwoonenone 351221106939suppose that a married couple is selected at random.(a) use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (enter your answers to 2 decimal places.)0 1 2 3 4(b) do the probabilities add up to 1? why should they? yes, because they do not cover the entire sample space. no, because they do not cover the entire sample space. yes, because they cover the entire sample space. no, because they cover the entire sample space. what is the sample space in this problem? 0, 1, 2, 3 personality preferences in common1, 2, 3, 4 personality preferences in common 0, 1, 2, 3, 4, 5 personality preferences in common0, 1, 2, 3, 4 personality preferences in common2. m& m plain candies come in various colors. according to the m& m/mars department of consumer affairs, the distribution of colors for plain m& m candies is as follows. color purple yellow red orange green blue brownpercentage 20% 18% 17% 9% 9% 10% 17%suppose you have a large bag of plain m& m candies and you choose one candy at random.(a) find p(green candy or blue candy).are these outcomes mutually exclusive? why? yes. choosing a green and blue m& m is not possible. no. choosing a green and blue m& m is not possible. no. choosing a green and blue m& m is possible. yes. choosing a green and blue m& m is possible.(b) find p(yellow candy or red candy).are these outcomes mutually exclusive? why? yes. choosing a yellow and red m& m is possible. no. choosing a yellow and red m& m is not possible. yes. choosing a yellow and red m& m is not possible. no. choosing a yellow and red m& m is possible.(c) find p(not purple candy).3. when do creative people get their best ideas? usa today did a survey of 966 inventors (who hold u. s. patents) and obtained the following information. time of day when best ideas occurtime number of inventors6 a. m.-12 noon12 noon-6 p. m.6 p. m.-12 midnight12 midnight-6 a. m. 284126332224(a) assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 a. m. to 12 noon, from 12 noon to 6 p. m., from 6 p. m. to 12 midnight, from 12 midnight to 6 a. m. (enter your answers to 3 decimal places.)6am-12pm 12pm-6pm 6pm-12am 12am-6amno, because they do not cover the entire sample space. yes, because they cover the entire sample space. yes, because they do not cover the entire sample space. no, because they cover the entire sample space.(b) do the probabilities add up to 1? why should they? what is the sample space in this problem? 12am-12pm6am-6pm 6am-12amthe entire day