Probability Problems with Employee Data and Museum Visitors
Solve various probability problems involving employees in a company and museum visitors based on provided data tables and scenarios. Calculate probabilities for different events such as being female, male and a manager, age groups, and zone visits. Understand and apply set notation in Venn diagrams.
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Probability Probability
1 The two-way table shows the breakdown of employees in a company. Find the probability that an employee is female. ??? ???
2 The two-way table shows the breakdown of employees in a company. Find the probability that an employee is male and a manager. ?? ???= ? ???
3 A random sample of 500 visitors to 4 zones of a museum were asked their age in years. The results are summarised in the table below. Find the probability that a visitor chosen at random was over 35 and visited the green or orange zone. ??? ???= ?? ???
4 A random sample of 500 visitors to 4 zones of a museum were asked their age in years. The results are summarised in the table below. Find the probability that a visitor chosen at random is under 19. ?? ???= ?? ???
5 A random sample of 500 visitors to 4 zones of a museum were asked their age in years. The results are summarised in the table below. Find the probability that a visitor chosen at random did not go to the blue zone. ??? ???=?? ??
6 How would the shaded area in the Venn diagram be written in set notation? ? ? ? (? ?) ? ?
7 The Venn diagram shows information about the 1000 students who study either full-time or part-time at a college. E F 450 264 94 132 In the diagram: ? represent the students who study full-time ? represents the students who study engineering How many students study engineering part-time? 94 358 170 264
8 The Venn diagram shows information about the 1000 students who study either full-time or part-time at a college. E F 450 264 94 132 In the diagram: ? represent the students who study full-time ? represents the students who study engineering How many students study engineering full-time? 94 358 170 264
9 The probabilities of events ?, ? and ? are related, as shown in the Venn diagram below. C A B 0.18 0.03 0.22 0.11 0.27 ? Find the value of ?. 0.51 0.19 0.49 0.81
10 Determine which of the following statements is most true for the event A student passes both A-level Maths pure exam papers . Independent and not mutually exclusive Independent and mutually exclusive Not independent and not mutually exclusive Not independent and mutually exclusive
11The events A and B are such that ? ? = 0.35 and ? ? = 0.5. ? and ? are mutually exclusive. Find ?(? ?). ?.??
12 The events A and B are such that ? ? =2 2 30 . 9 , ? ? =3 5 and ? ? ? = Are ? and ? mutually exclusive events? No as ?(? ?) ?.
13 The events A and B are such that ? ? =2 2 21 . 9 , ? ? =3 7 and ? ? ? = Are ? and ? independent events? Yes as ? ? ? ? =? ? ? ? ??= ?(? ?). ?=
14 On a Saturday night Peter and Paula always order one of three types of meal from the chip shop: Fish and chips, sausage and chips or chicken and chips. Their choices from week to week are independent of each other. The probability that they order chicken and chips is 2 5 . The probability that they order fish and chips is 3 7 . Find the probability that Peter and Paula order sausage and chips. ? ? = ? ? ? ? ? ?= ??
15 On a Saturday night Peter and Paula always order one of three types of meal from the chip shop: Fish and chips, sausage and chips or chicken and chips. Their choices from week to week are independent of each other. The probability that they order chicken and chips is 2 5 . The probability that they order fish and chips is 3 7 . In a period of three consecutive Fridays, find the probability that Peter and Paula order chicken and chips on all three Saturdays. ? ? ? ? ? ?&? ?? ??? ? = = ???
16 A bag contains 7 blue discs, 6 red discs and 1 yellow disc. Two discs are drawn at random from the bag without replacement. Find the probability that exactly one of the discs is red. ? ? ? ??=?? ? ? ??? ???? = ?? ??+ ?? ??
