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