Terry is proud of the vast array of colours in his new bag of 144 crayons. Billy feels a little envious, having only 48 crayons in his pencil case. But he believes he has a better chance than Terry of choosing a red-shaded crayon if each boy pulls a crayon from his pencil case without looking. Each boy has 12 different colours: brown, black, red, blue, yellow, green, orange, purple, white, grey, silver, and gold. Terry’s set contains 12 different shades of each colour, while Billy’s set contains 4 different shades of each colour. a) What is the theoretical probability of Terry choosing a red-shaded crayon? b) What is the theoretical probability of Billy choosing a red-shaded crayon? c) Is Billy correct in believing he stands a better chance than Terry? All solutions must be submitted by noon time on Friday, April 10th. Please remember: •First and Last NameClass•Problem of the Week #•Answer done on a sheet of looseleaf (folded in fourths in order to fit into the ballot box outside of the Math Center on the Orange Team floor.)•Show how you found your answer (answer only will not be eligible for draw)•Put your answer in a summative phrase (sentence form) with a circle around it (makes it clearer for the judges)•Make sure your work is neat (the winner's solution will be posted on the website)