If the bet is done 762 times then expected value is that we may have a loss of $1562.1if the bet is that is heart comes we will get $16 and lose $3 if not comes.
Given We will get $16 if hearts come and lose $3 when not comes and bet is made 762 times. We have to calculate the expected win after 762 times.
We know that there are 13 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 13/52*12/51
=156/2652
=0.05
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-0.05
=0.95
When bet is made only 1 time expected value will be 0.05*16-0.95*3
=0.8-2.85
=-2.05 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -2.05*762=-1562.1.
Hence the expected value when bet is made 762 times is that we will lose $1562.1 .
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