Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level80. Tree Diagrams1. The probability that Sarah will win the long jumpis 0.1 and, independently, the probability that shewill win the 100 metres is 0.15.a) Complete the tree diagram to show all thepossible outcomes.b) What is the probability that she wins one orboth events?c) What is the probability that she wins neitherevent?Long jumpWinNot win100 metresWn/wW2. William waits at the bus stopeach morning in order tocatch the bus to work. Somemornings his friend arrives inhis car and gives him a ride towork. From past experiencethe probabilities of Williamgetting the bus is 0.7 and theprobability that he gets a ridewith his friend is 0.3. Whenhe gets the bus, the chance of him being late for work is 0.05 and when he gets a ride thechance of him being late is 0.15.a) Complete the tree diagram to show all the possible outcomes.b) From the diagram calculate the probability that on a day chosen at random he will be late.3. A bag contains 5 greensweets and 3 red sweets.Two sweets are withdrawnat random from the bag.a) Complete the diagram toshow all the possibleoutcomesb) What is the probabilityof getting:(i) a sweet of each colour(ii) at least one red sweet?1st sweet4. A bag contains 8 discs, 4black and 4 white. 2 discsare removed at randomfrom the bag. By drawing a tree diagram calculate the probability that:a) both discs will be black b) at least one of the discs will be white.5. In class 7B, two pupils are chosen at random from the class register to be the monitors.There are 12 boys and 16 girls in the class. By drawing a tree diagram calculate theprobability that:a) the two people chosen will be girls b) the two people chosen will be boysc) one person of each gender will be chosen.BusCarRedsweetGreensweetLate2nd sweetn/w0.7 × 0.05 = 0.035Red3 2-- × --8 7=3-----28