4. A sports club has 80 members. For the three activities Swimming (S), Cycling (C) and Running (R), 8 members take part in all three activities, 3 members do not take part in any of the three activities, 22 members take part in only Swimming, 23 members take part in Swimming and Cycling, 19 members take part in Swimming and Running, 14 members take part in Cycling and Running. a) Using this information place the number of members in the appropriate subsets of the Venn diagram. 3 The number of members who take part in only Cycling is twice the number of members who take part in only Running. Let the number of members who take part in only Running be r and, using all the given information, b) form an equation in x. c) Solve your equation to find the value of x. 2 Manuel is in the set (R U C)' s. d) Write down which of the three activities Manuel takes part in. c) Write down i) n(C), ii) n[S N(R U C)J. A member of the sports club is to be chosen at random. Given that this member takes part in Cycling, O find the probability that this member also takes part in both Swimming and Running.

4. A sports club has 80 members. For the three activities Swimming (S), Cycling (C) and Running (R), 8 members take part in all three activities, 3 members do not take part in any of the three activities, 22 members take part in only Swimming, 23 members take part in Swimming and Cycling, 19 members take part in Swimming and Running, 14 members take part in Cycling and Running. a) Using this information place the number of members in the appropriate subsets of the Venn diagram. 3 The number of members who take part in only Cycling is twice the number of members who take part in only Running. Let the number of members who take part in only Running be r and, using all the given information, b) form an equation in x. c) Solve your equation to find the value of x. 2 Manuel is in the set (R U C)' s. d) Write down which of the three activities Manuel takes part in. c) Write down i) n(C), ii) n[S N(R U C)J. A member of the sports club is to be chosen at random. Given that this member takes part in Cycling, O find the probability that this member also takes part in both Swimming and Running.

Name: 4. A sports club has 80 members.For the three activities Swimming (S)
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Description: 4. A sports club has 80 members.For the three activities Swimming (S),Cycling (C) and Running (R),8 members take part in all three activities,3 members do not take part in any of thethree activities,22 members take part in only Swimming,23 members t

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

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4. A sports club has 80 members.
For the three activities Swimming (S),
Cycling (C) and Running (R),
8 members take part in all three activities,
3 members do not take part in any of the
three activities,
22 members take part in only Swimming,
23 members take part in Swimming and
Сycling,
19 members take part in Swimming and
Running,
14 members take part in Cycling and
Running.
a) Using this information place the number
of members in the appropriate subsets of
the Venn diagram.
22
3
The number of members who take part in only Cycling is twice the number of members who take part
in only Running. Let the number of members who take part in only Running be r and, using all the
given information,
b) form an equation in x.
c) Solve your equation to find the value of x.
2
Manuel is in the set (R U C)' s.
d) Write down which of the three activities Manuel takes
part in.
c) Write down
i) n(C),
ii) n[S N(R U C)J.
A member of the sports club is to be chosen at random. Given that this member takes part in Cycling,
O find the probability that this member also takes part in both Swimming and Running.

2. A coin is biased so that the probability of throwing a tail is . The coin is to be tossed three
times.
Calculate the probability of
a) throwing two heads followed by one tail,
b) throwing two tails and one head in
any
order.
3
C.

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