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You are taking a multiple-choice test that has 8 questions. Each of the questions has 4 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions? You can answer the questions in \( \square \) ways.

Ask by Mcdonald Bowen. in the United States
Mar 18,2025

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You can answer the questions in 65,536 ways.

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Mind Expander

To find out the total number of ways to answer the 8 questions, think of it this way: each question has 4 possible answer choices, and you're making a choice for each of the 8 questions. Therefore, the total number of ways to answer the questions is calculated by raising the number of choices (4) to the power of the number of questions (8). This gives you \( 4^8 \). Now, if you do the math, \( 4^8 = 65536 \). So, you can answer the questions in 65,536 different ways. That's like having a massive deck of cards, where each question is like drawing a card from one of four decks. Keep shuffling those choices! The number of combinations you can create with such scenarios demonstrates just how exponential growth works in decision-making! Next time you're faced with multiple choices, think about how quickly options can multiply—just like the fun of trying to shuffle a massive playlist for a party!

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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