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230 PROBABILITY (Chapter 10) EXERCISE 10F 1 Two coins are tossed simultaneously. Use a 2-dimensional grid to illustrate the sample space and hence determine the probability of getting: a two tails b a head and a tail c at least one tail. 2 A coin and a die are tossed simultaneously. Draw a 2-dimensional grid to illustrate the sample space. Determine the probability of getting: a a tail and a 6 c neither a 2 nor a 6 e a head and an odd number b a tail or a 6 d neither a tail nor a 5 f a head or an odd number. 3 Draw a 2-dimensional grid to illustrate the sample space when an ordinary die is tossed and a triangular spinner labelled A, B and C is spun simultaneously. Hence, determine the probability of getting: a B and 5 c a non-B and a multiple of 3. b A and a prime number 4 A pair of dice is rolled. The 36 different possible âpair of diceâ results are illustrated on the 2-dimensional grid alongside. Use the grid to determine the probability of getting: a two 3s c a 5 or a 6 e exactly one 6 die 2 6 5 4 3 b a 5 and a 6 d at least one 6 f no sixes 2 1 1 g a sum of 7 h a sum of 7 or 11 i a sum greater than 8 2 3 4 5 die 1 6 j a sum of no more than 8. G COMPOUND EVENTS Consider the following problem: Box X contains 2 blue and 2 green balls. Box Y contains 3 red and 1 white ball. A ball is randomly selected from each of the boxes. Determine the probability of getting a blue ball from X and a red ball from Y. B R R = 38 : R box X 95 50 75 B 25 0 5 95 100 50 75 25 0 5 95 50 75 25 0 5 95 100 50 75 25 0 5 100 magenta R W Y box Y In the investigation that follows, we will seek a quicker, easier way to find this probability. cyan R W yellow Y:\HAESE\IB_MYP4\IB_MYP4_10\230IB_MYP4_10.CDR Tuesday, 18 March 2008 1:32:44 PM PETERDELL 100 6 16 R G G X By illustrating the sample space on a twodimensional grid as shown alongside, we see that 6 of the 16 possibilities are blue from X and red from Y. Since each outcome is equally likely, P(blue from X and red from Y) = B black B G G IB MYP_4