Jimmy rolled a die 90 times and recorded the results. He got a one 15 times, a two 22 times, a three 18 times, a four 11 times, a five 13 times and a six 11 times. Using his results how many six's could Jimmy expect if he rolled the die 1500 times?

Since in Jimmy's 90 times die roll six appeared 11 times, so the probability of face of sixes appearing is: [tex] \frac{11}{90} [/tex].Thus , when the die is rolled 1500 times then it is obvious that the number of times the face of six will appear will also increase proportionately.This proportionate increase in the number of times the face of six will appear will be given thus:If six appears 11 times in 90 rolls then to find how many times it will appear in 1500 rolls is calculated as [tex] \frac{11}{90}=\frac{x}{1500} [/tex] where x is the number of times the face of six will appear.Thus, expression gives:[tex] x=\frac{11}{90}\times 1500=\frac{11\times 50}{3}=\frac{550}{3} \approx 183 [/tex]Therefore, Jimmy can six's approximately 183 times if he rolled the die 1500 times.