On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of (a) Being correct only on questions 1 and 4 (i. e., scoring C, I, I, C, I, I). (b) Being correct on two questions.

(a) 1.64%

(b) 24.58%

Step-by-step explanation:

As for each question there are one correct answer in five possible answers, the probability of guessing the correct answer is 1/5 = 0.2, so the probability of guessing the wrong answer is (1 - 0.2) = 0.8.

(a) The probability of being correct only on questions 1 and 4 is calculated multiplying all the following probabilities:

question 1 correct: 0.2

question 2 wrong: 0.8

question 3 wrong: 0.8

question 4 correct: 0.2

question 5 wrong: 0.8

question 6 wrong: 0.8

P = (0.2)^2 * (0.8)^4 = 0.0164 = 1.64%

(b) The probability of being correct in two questions is calculated similarly to the question in (a), but now we also have a combination problem: The 2 correct questions can be any group of 2 questions inside the 6 total questions, so we also multiply the probability of each question being correct or wrong by the combination of 6 choose 2:

C(6,2) = 6!/(4!*2!) = 6*5/2 = 15

P = 15 * (0.2)^2 * (0.8)^4 = 0.2458 = 24.58%

4038

step-by-step explanation:

pleaze mark brainliest!

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3