a radio program has a quiz consisting of 3 multiple choice questions, each with 3 choices. A contestant wins if he or she gets 2 or more of the questions right. The contestant answers randomly to each question. What is the probaility of winning?

Answer 1

p right = .5
1-p right = .5
n = 3
r = 2

C(3,2) = 3!/[ 2!(3-2)!] = 3
P(3,2) = C(3,2) .5^2 .5^1

= 3 * .5^3

Answer 2

prob(right) = 1/3
prob(wrong) = 2/3

prob(2 of 3 correct)
= C(3,2) (1/3)^2 (2/3)
= 3(1/9)(2/3)
= 2/9

prob(getting all 3 correct)
= (1/3)^3 = 1/27

prob(win) = 2/9 + 1/27 = 7/27

checking:
prob(none right) = (2/3)^3 = 8/27
prob(one right) = 3(1/3)(2/3)^2 = 4/9

from above:
prob(two right) = 2/9
prob(3 right) = 1/27

they should add up to 1
8/27 + 4/9 + 2/9 + 1/27 = 27/27 = 1
All is good.

Answer 3

oh, forgot to add prob of getting all three
which is .5^3
so total = 4 * .3^3

Answer 4

Also the prob of a choice being correct is 1/3 not 1/2

Answer 5

Sorry, missed that sentence