WorkSHEET 3.3 Probability III Name: In the Lotto draw there are numbered balls. Find the probability that the first number drawn is: (a) a (b) a (d) even odd (e) greater than 40. Using: (a) P() = (b) P() = 22 P(even) = P = WO PO (d) 23 P(odd) = (e) 5 P(greater than 40) = = 9 2 A bag contains 3 white balls, 4 red balls, 5 black balls, 6 green balls and 7 yellow balls. A single ball is drawn from the bag. What is the probability that it is neither white nor black? Total number of marbles = 3 + 4 + 5 + 6 + 7 = 25 Number of white or black = 3 + 5 = P(white or black) = 25 7 Therefore, P(neither white nor black) = 25 3 Consider the following table, showing the number of cars repaired by 5 different mechanics during a day. Mechanic Cars fixed 2 5 3 2 4 22 5 6 A customer returns his car because it was not repaired properly. Without knowing which mechanic worked on it, determine the probability that it was mechanic. Total number of cars repaired = + 5 + 2 + 22 + 6 = 73 Mechanic repaired cars. P(car repaired by mechanic ) = 73 John Wiley & Sons Australia, Ltd 202 Page
4 Consider the following table showing voter preferences in all 6 Australian states. Labor Liberal Greens QLD 340 620 90 NSW 560 442 29 VIC 6 59 2 TAS 307 49 67 SA 47 462 226 WA 72 423 7 Total number in the survey = 76 Greens supporters = 9 9 Relative frequency = 76 599 = 354» 0.67 (about in 6 voters) Determine the relative frequency of Greens supporters. 5 Using the table in question 4, if a voter who participated in the survey is chosen at random, find the probability (as a decimal correct to 2 decimal places) that: (a) they supported the Labor party (b) they supported the Liberal party they are a Greens supporter from Victoria. 305 (a) P(Labor) = 76 = 0.42 2955 (b) P(Liberal) = 76 = 0.4 2 P(Greens) = 76 = 0.03 John Wiley & Sons Australia, Ltd 202 Page 2
6 In a class of 40 students, 2 liked both fish and meat, and 6 liked neither. If there were a total of 25 who liked meat, construct a Venn Diagram of this situation. Put a 6 outside the two circles, and a 2 at the intersection. Since there were 25 who liked meat, there were 25 2 = 3 who liked meat but not fish. Put this 3 in the left circle. The remaining number is calculated from 40 2 6 3 = 9 7 Two dice are rolled, and the outcome is a pair of numbers. Determine the probability that the sum of the two dice is given that their total is greater than 6. There are 36 outcomes, 2 of which have a total greater than 6. There are 5 of these outcomes which have a total of. P(total of total greater than 6) = 5 2 From a standard deck of cards, determine the probability of drawing: a) 6 b) 7 c) 6 or 7 d) club e) diamond f) club or diamond Using P = %& a) P = ( = + )* +, b) P = ( = + )* +, Using P A B = P A + P(B) c) P = + +, + + +, = * +, d) P = +, )* = + ( e) P = +, )* = + ( f) P = + ( + + ( = * ( = + * John Wiley & Sons Australia, Ltd 202 Page 3
9 You have to roll a die and toss a coin. What is the probability that you roll an even number and toss a head? Using: P = %& P even = 3 6 = 2 P head = 2 Use: P A B = P(A) P(B) P even head = P(even) P(head) = 2 2 = 4 0 As per Question 9. But now you have to toss the coin twice. What is the probability that you roll an even number and toss two heads? Using: P = %& P even = 3 6 = 2 P head = 2 Use: P A B = P(A) P(B) P even head = P(e) P(h) P(h) = 2 2 2 = There are 4 Red, 5 White and 3 Blue balls in a bag. You have to draw out a ball, replace it, and then select a second. Determine the probability that you pull out a red then a blue ball. Using P = %& And P A B = P(A) P(B) P Red Blue = 4 2 3 = 2 For two mutually exclusive events, if P A = + Using:, and P B = + calculate P A B. ) P A B = P A + P B P A B = 3 + 5 = 5 John Wiley & Sons Australia, Ltd 202 Page 4
3 You draw a card from a standard deck. What is the chance it is an Ace or an even numbered card? Using: P A B = P A + P B, where P Ace = 4 52 P even card = 20 52 P Ace Even = 4 52 + 20 52 = 6 3 4 For two independent events, if P A = +, and Using: P B = + calculate P A B. ) 5 You flip a coin and throw a die. What is the probability you toss a Head and roll an even number? P A B = P A P B P A B = 3 5 = 5 Using: P A B = P A P B, where P Head = 2 P even = 3 6 P Head Even = 2 3 6 = 4 John Wiley & Sons Australia, Ltd 202 Page 5