Suppose that Nacho takes a multiple choice test. The test has 4 questions. Each question has 2 choices. What is the probability that Nacho will get all 4 questions wrong?

Question

Probability - statistics

Answer 1

(1/2)^4 = 1/16 = probability of getting all 4 wrong= .0625 = 6.25%

1/16 chance of all 4 right

1/4 1 right, 3 wrong

1/4 1 wrong, 3 right

3/8 chance of 2 wrong 2 right

use Pascal's Triangle

1

11

121

1331

14641 as numerators, denominators=1+4+6+4+1 = 16

1/16, 4/16, 6/16, 4/16, 1/16 for P(0R), P(1R), P(2R), P(3R). P(4R)

P(4R)= Probability of 4 Right = Probability of zero Wrong

P(0R) = Probability of 0 Right,= Probability of 4 Wrong

or

4C4(1/2)^4, 4C3(1/2)^4, 4C2(1/2)^4, 4C1(1/2)^4, 4C0(1/2)^4

4C4 = 4!/4!1! = 1

4C4(1/2)^4 = 1(1/16) = 1/16