HotPinkGirl one year ago 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

1. HotPinkGirl

@Hero @DullJackel09 @micahm

2. HotPinkGirl

@Nnesha @sammixboo @johnweldon1993 @dtan5457

3. johnweldon1993

So what are our possible outcomes of flipping 2 coins? H,H H,T T,H T,T right?

4. HotPinkGirl

right : )

5. johnweldon1993

So, a total of 4 ways for the game to go In how many ways...will she get exactly 1 H?

6. HotPinkGirl

2 ways?

7. 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?

8. HotPinkGirl

1

9. 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

10. 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 $\large EV = \frac{1}{2} \times 4 + \frac{1}{4} \times 6 = ?$

11. HotPinkGirl

how do you do that?

12. johnweldon1993

How did I get to that equation? Or just how to calculate it?

13. HotPinkGirl

how do you calculate it?

14. johnweldon1993

Oh okay So what is 1/2 times 4? and what is 1/4 times 6?

15. HotPinkGirl

2+3 = 5?

16. 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?

17. HotPinkGirl

2+3/2 = 3

18. johnweldon1993

Not quite :) $\large 2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2} = ?$

19. HotPinkGirl

3.5

20. HotPinkGirl

is the answer B. 3 1/2?