Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level78. Probability 21. A bag contains 3 black discs and 7 white discs. A disc is taken at random from the bag andnot replaced. This is carried out three times. Calculate the probability of getting:a) a black disc on the first drawb) a black disc followed by a white discc) a black disc followed by two white discs.2. It is known from past experience that of every 350 students entered for a typing examination280 will pass the first time. Of those that fail, 80% of them pass on their second attempt.What is the probability that a student, chosen at random from a group of students sitting theexamination for the first time, will pass on the first or second attempt?3. The probability that there will be passengers waiting to be picked up at a bus stop is 0.85. Along distance bus has 3 stops to make. Calculate the probability that it will have to pick uppassengers one or more times on its journey.4. In a game of chance, two people each have a dice numbered 1, 1, 1, 2, 2, 2. They both throwthe dice together. If both the outcomes are the same, then they have a second try. If they arethe same again, then they have a third try, and so on until someone gets a 2 while the othergets a 1. The winner is the person who gets the 2.a) What is the probability that the game is over on the first pair of throws?b) What is the probability that someone wins on the second pair of throws?5. In a class of 30 pupils there are 14 boys and 16 girls. Two names are chosen at random.Calculate the probability that:a) the first name selected is a girls’b) both the names selected are girls’.6. In a bag there are 5 discs, 3 red and 2 blue. The red discs have the numbers 1, 2 and 3written on them and the blue discs have the numbers 1 and 2 on them.1 2 3 1 2Red DiscsBlue discsa) What is the probability of withdrawing a disc with a 2 on it from the bag?b) Two discs are drawn from the bag. What is the probability that one disc has a 2 on it andone disc is red?7. An engineering works produces metal rods. The rods are 6.2cm long and 0.5mm indiameter, both dimensions to the nearest 0.1mm. When the rods are inspected there can befour different outcomes:either one or both dimensions are under size, in which case the rod is scrapped,or one dimension is oversize and one is correct, in which case it is reworked,or both dimensions are oversize, in which case the rod is reworked,or both dimensions are correct, in which case the rod is acceptable.It is known from past experience that 1.2% are under size in length and 1.5% are under sizein diameter. Also 2.5% are oversize in length and 2.2% are oversize in diameter.A rod is selected at random. What is the probability that it is:a) scrapped b) reworked c) accepted?