A section of an exam contains four True-False questions A student who did not st

Question

A section of an exam contains four True-False questions A student who did not study takes this exam and randomly guesses on these four questions. using the multiplication rule, how many different ways can four questions be out randomly by the student? Construct the sample space using a tree diagram. Use T or True and F for False Assuming the outcomes to be equally likely find the probability that all the answer are "True" (Give reduced fraction)___________ Assuming the outcomes to be equally likely find the probability that exactly one of the fours answer is "True". (Give reduced fraction) ________ Assuming the outcomes to be equally likely, find the probability that exactly two answers are and two answer are "False". (Give reduced fraction) _________

Explanation / Answer

An answer can be given in 2 ways: T or F.

There is a probability of 1/2 to get either a TRUE or FALSE.

6.

a.This can be done in 2*2*2*2 = 16 ways
b. The sample space is given by:

TTTF TFFT FFFF TFTT
TFTF FTTF TTTT TFFF
FFFT FFTT FTTT TTTF
FTFT TTFF FTFF FFTF

c. P( all true) = TTTT/16 = 1/16
d.P( oneof them is T) = FFFT FFTF FTFF TFFF / 16 = 1/4
e. P( exatly 2 are TRUE) = 4C2/16 = 3/8

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