Question 1191674: Mason plays a game by flipping two fair coins. He wins the game if both coins land facing heads up. If Mason plays 300 times, how many times should he expect to win? Enter your answer in the box.
Im a little confused on this problem because technically it would be 300 / 2 = 150. yet when i submitted my hw i got it wrong i want to know what i did wrong can someone guide me through the steps?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
If Mason had 1 coin, then the sample space is {H,T}
The sample space is the set of all possible outcomes.
H = heads
T = tails
If Mason had 2 coins, then the sample space is
{HH, TH, HT, TT}
Which I find easier to represent in the form of a two-way table like this
Not only is the table handy to organize all the items in the sample space, but it visually shows why multiplication is used to count all possible outcomes (2*2 = 4).
Let's calculate the probability of getting the outcome HH
That's as simple as noticing HH shows up 1 time out of 4 times total
Therefore,
P(HH) = 1/4
Or you could follow this pathway
P(H) = 1/2
P(HH) = P(H)*P(H)
P(HH) = (1/2)*(1/2)
P(HH) = 1/4
The second line is valid due to each coin flip being independent of one another.
If Mason plays 300 times, then he should expect to win 300*(1/4) = 300/4 = 75 times
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