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vodka
3 months ago
5

Krista has a quiz today. There are 4 questions with 4 options. Each question only has one correct answer. She wants to guess and

get 3 out of the 4 questions right. What is the probability of her getting 3 right​
Mathematics
1 answer:
zzz [12.3K]3 months ago
7 0

Answer:

The probability is calculated to be 0.258.

Step-by-step explanation:

This question seeks the likelihood of Krista answering exactly 3 correctly from her choices.

Each question has four answer options, totalling 4 questions.

The total options available equal 4 * 4 = 16.

Each question features one correct and three incorrect options, leading to 4 correct choices and 12 incorrectly possible selections.

The chance of picking a wrong option is 12/16 = 3/4, while the likelihood of selecting the correct one stands at 1/4.

We can apply a Bernoulli approximation to ascertain the chances of getting three correct answers.

Let p represent the probability of picking the correct option, while a represents the wrong option's probability.

The exact probability of achieving three correct answers can be computed as;

P(r = 3) = nCr p^r q^(n-r)

Where n indicates the total options and r signifies the number of correct ones chosen.

The probability = 12C3 * (1/4)^3 * (3/4)^9

= 220 * 0.015625 * 0.075084686279 = 0.258

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