Question

1.) Consider the experiment of flipping a fair coin 3 times, the result of each flip yielding either Heads (H) or Tails (T)

I) How many possible outcomes are there in the sample space?

II)) List all the possible outcomes in the sample space

III) Define event A to be the event that a single trial results in exactly 2 Heads

A=

P(A)=

Interpret P(A):

IV) Define event B to be the event that a single trail results in more Tails than Heads

B=

P(B)=

Interpret P(B):

V) Fill in the blanks with the best answer: Events A and B are said to be _________, allowing us to compute P(A U B)_________ double counting

A) not disjoint; without needing to worry about

B) disjoint; without needing to worry about

C) not disjoint; making sure to check for

D) disjoint; making sure to check for

VI) Define an event C that result in P(C)=0.5. Write a sentence defining event C

Answer 1

I))

number of outcomes = 2^{3 =}8

ii) possible outcomes = ( (HHH),(HTH),(THT),(TTT),(TTH),(HHT),(THH),(HTT))

III)

A : event of getting exactly 2 heads in single trial

P(A)= 3/8 = 0.375

INTERPRETATION: there is 0.37 chance that we get exactly 2 heads in single trial

iv)

B: event that a single trail results in more Tails than Heads

P(B)= 4/ 8 = .5

INTERPRETATION: there is 0.5 chance that we get more Tails than Heads

v)

Events A and B are said to be disjoint __, allowing us to compute P(A U B)__without needing to worry about_______ double counting

vi)

C:  event that a single trail results in more HEADS than tails

p(C): 4/8 = 0.5