Reading Questions 2

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Problem 1. 

Which of the following represents a valid probability table?
(i)
outcomes 1 2 3 4 5
probability 1/5 1/5 1/5 1/5 1/5
(ii)
outcomes 1 2 3 4 5
probability 1/2 1/5 1/10 1/10 1/10

 i
 ii
 i and ii
 Not enough information
  

Problem 2. 

A sample space has exactly two outcomes. The first has probability p and the second has probability 3p. What is the value of p?

 


Problem 3. 

Let A and B be two events with P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.3. What is P(A ∪ B)?
(Hint: visualize with Venn diagrams.)

 0.5
 0.6
 0.7
 0.8
 0.9
  


Problem 4. 

Our experiment consists of tossing a coin 3 times. Take the sample space to be all sequences of 3 heads or tails.

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For each of the following give the size of the event.

(i) The event 'there are more heads than tails'.


 0
 1
 2
 3
 4
 5
 6
 7
 8
  

(ii) The event 'the first heads occurs after the first tails.'


 0
 1
 2
 3
 4
 5
 6
 7
 8