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mathmari

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A multiple choice test consists of 10 questions. For every question there are five possible answers, of which exactly one is correct. A test candidate answers all questions by chance.

(a) Give a suitable random variable with value range and probability distribution in order to work on part (b) with it.

(b) Determine (with intermediate steps) the probability that

(i) exactly 4 questions were answered correctly,

(ii) more than 4 questions have been answered correctly,

(iii) all tasks have been answered correctly,

(iv) at least half of the questions were answered correctly,

(v) at least 5 and at most 8 questions have been answered correctly.For (a) :

Let $X$ be a random variable that describes the number of correct answers out of $10$, right?

For each correct answer the probability is equal to $\frac{1}{5}$ and each wrong answer has the probability $\frac{4}{5}$.

Is that correct so far? :unsure: