HotPinkGirl
  • HotPinkGirl
olivia tossed two fair two sided coins. in a game, she earns 4 points if exacly one coin lands on heads and 6 points if both coins land on heads. if points are not earned for tails, what is the expected value of the points earned? A. 3 1/3 B. 3 1/2 C. 5 D. 6
Mathematics
schrodinger
  • schrodinger
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HotPinkGirl
  • HotPinkGirl
HotPinkGirl
  • HotPinkGirl
johnweldon1993
  • johnweldon1993
So what are our possible outcomes of flipping 2 coins? H,H H,T T,H T,T right?

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HotPinkGirl
  • HotPinkGirl
right : )
johnweldon1993
  • johnweldon1993
So, a total of 4 ways for the game to go In how many ways...will she get exactly 1 H?
HotPinkGirl
  • HotPinkGirl
2 ways?
johnweldon1993
  • johnweldon1993
Right! Either H,T or T,H good So there are 2 ways of getting just 1 H....so that probability is 2/4 or 1/2 right? Now, how many ways will she get both H?
HotPinkGirl
  • HotPinkGirl
1
johnweldon1993
  • johnweldon1993
Right again So out of the 4 ways of the game ending...we have just 1 in that way...so that probability is 1/4
johnweldon1993
  • johnweldon1993
SO! Now to find the expected value...we take the probability of each event with the points from those events... \[\large EV = \text{Probability of 1 H}\times \text{Points} + \text{Probability of 2H} \times \text{Points}\] So \[\large EV = \frac{1}{2} \times 4 + \frac{1}{4} \times 6 = ?\]
HotPinkGirl
  • HotPinkGirl
how do you do that?
johnweldon1993
  • johnweldon1993
How did I get to that equation? Or just how to calculate it?
HotPinkGirl
  • HotPinkGirl
how do you calculate it?
johnweldon1993
  • johnweldon1993
Oh okay So what is 1/2 times 4? and what is 1/4 times 6?
HotPinkGirl
  • HotPinkGirl
2+3 = 5?
johnweldon1993
  • johnweldon1993
I'm assuming the 2 was the answer to the 1/2 times 4...which yes is correct however...does 1/4 x 6 = 3? I get 6/4 or 3/2 right? So what is 2 + 3/2?
HotPinkGirl
  • HotPinkGirl
2+3/2 = 3
johnweldon1993
  • johnweldon1993
Not quite :) \[\large 2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2} = ?\]
HotPinkGirl
  • HotPinkGirl
3.5
HotPinkGirl
  • HotPinkGirl
is the answer B. 3 1/2?

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