Question

In a multiple-choice test, each question has four options. Students will get 10 points for each correct answer; lose 4 points for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value.

Answer 1

each has probability 1/4 = .25
multiply and add.
if you don't guess you get nothing.
if you do guess you are right 1/4 of the time and gain 10 points, are wrong 3/4 of the time and lose 4 points
so if you guess expected value is
\[10\times \frac{1}{4}-4\times \frac{3}{4}=\frac{10-12}{4}=\frac{-2}{4}=-\frac{1}{2}\]

Answer 2

on average each guess loses you half a point. don't guess

Answer 3

hello.... master!

Answer 4

howdy :)

Answer 5

how'd i do here? hope it is clear

Answer 6

i take you two know each other. LOL!!

Answer 7

intimate friends, whoever he is

Answer 8

lol! what

Answer 9

...... know who? :)

Answer 10

you two

Answer 11

who knows? ;)

Answer 12

lol.... i feel like this should be my dojo. Wax on, wax off...

Answer 13

the waxer

Answer 14

i meant my the greeting that you two gave to each other. keep up with the pace people.

Answer 15

..if you can take this peeble from my hand; then... no,no,no... i wasnt ready!

Answer 16

is it my fault site is so slow?
ahh very good grasshopper...

Answer 17

life is like ball of string...

Answer 18

satellite, go.. bring me soup; but DONT touch it lol

Answer 19

you two are a VERY interesting match.

Answer 20

:) didja get your answer for the value question

Answer 21

yeah its -1/2 right and it would be to her disadvantage to guess

Answer 22

good :)

value*probability + value*probability + .... = solution

Answer 23

10×1/4 −4×3/4 =10−12/ 4 =−2/4 = -1/ 2