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24. For the Sample space \( S=\{1,2,3,4,5,6,7,8\} \) i. Write down a simple event. ii. Write down a composite event.

Ask by Vargas Schneider. in the United Kingdom
Mar 10,2025

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i. A simple event: {3} ii. A composite event: {2, 4, 6, 8}

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Bonus Knowledge

A simple event in the sample space \( S=\{1,2,3,4,5,6,7,8\} \) could be the occurrence of rolling a die and getting the outcome 4, represented as the event \( E=\{4\} \). This is a single outcome from the sample space. A composite event could involve multiple outcomes, such as rolling an even number. This can be represented as the event \( E=\{2,4,6,8\} \), which includes several outcomes from the sample space, making it composite because it consists of more than one simple event.

Related Questions

1. On a single toss of one die, find the probability of obtaining a) The number 4 b) an odd number c) an even number d) a number less than 4 e) a number greater than 4 f) an odd or an even number 2. In a junior school class of 28 pupils, 7 are in both a sports team and the school band. There are 16 pupils involved in sports teams and 10 in the school band. Find the probability that a pupil chosen at random. a) is only in the school band b) is in either a sports team or the school band c) is in neither a sports team nor the school band 3. An integer is selected randomly from a set of integers \( \{1,2,3,4,5,6,7,8,9,10,11,12\} \). Find the probability that the integer is a) an even number or is divisible by 3 b) an even number and is not divisible by 3 c) not an even number and is not divisibleby 3 . 4. For the sample space \( S \), it is given that \[ \begin{array}{c} P(A)=0.5 \\ P(A \cup B)=0.6 \\ P(A \cap B)=0.2 \end{array} \] Find: a) \( P(B) \) b) \( P\left(A^{\prime} \cap B\right) \) c) \( P\left(A \cap B^{\prime}\right) \) d) \( P\left(A^{\prime} \cap B^{\prime}\right) \) 5. \( \quad C \) and \( D \) are two events where \( P(C)=0.1, P(D)=0.2 \) and \( P(C \cup D)=0.3 \). a) Determine whether \( C \) and \( D \) are two mutually exclusive events. b) Find \( P\left(C^{\prime}\right) \) and \( P\left(C^{\prime} \cap D^{\prime}\right) \) 6. The events \( A, B, C \) and \( D \) are mutually exclusive with \( P(A)=P(B)=0.3 \) and \( P(C)= \) \( P(D)=0.1 \). If \( E \) and \( F \) are events defined by \( E=A \cup D \) and \( F=B \cup C \), find a) \( P(E \cup F) \) b) \( P(E \cap F) \)
Probability Malaysia Mar 18, 2025

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