Question

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

Answer 1

@Hero @DullJackel09 @micahm

Answer 2

@Nnesha @sammixboo @johnweldon1993 @dtan5457

Answer 3

So what are our possible outcomes of flipping 2 coins?

H,H
H,T
T,H
T,T right?

Answer 4

right : )

Answer 5

So, a total of 4 ways for the game to go

In how many ways...will she get exactly 1 H?

Answer 6

2 ways?

Answer 7

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?

Answer 8

1

Answer 9

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

Answer 10

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

\[\large EV = \frac{1}{2} \times 4 + \frac{1}{4} \times 6 = ?\]

Answer 11

how do you do that?

Answer 12

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

Answer 13

how do you calculate it?

Answer 14

Oh okay

So what is 1/2 times 4?

and what is 1/4 times 6?

Answer 15

2+3 = 5?

Answer 16

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?

Answer 17

2+3/2 = 3

Answer 18

Not quite :)

\[\large 2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2} = ?\]

Answer 19

3.5

Answer 20

is the answer B. 3 1/2?