itomath.com

Expectation

A fair 6-sided die

Roll a fair 6-sided die.
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$P\left(\text{rolling a 3}\right)=\frac{1}{6}$

If you rolled a fair 6-sided die six times, how many times would you expect to roll a 3?

If you rolled a fair 6-sided die twelve times, how many times would you expect to roll a 3?

If you rolled a fair 6-sided die 54 times, how many times would you expect to roll a 3?

If you rolled a fair 6-sided die 9 times, how many times would you expect to roll a 3?

Notice how the expected number of times can be a value that is not possible.

A deck of cards

Pick one random card from the deck.
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$P\left(♥\right)=\frac{13}{52}=\frac{1}{4}$

If you picked one random card from the deck eight times, how many times would you expect to pick a ♥?

If you picked one random card from the deck 52 times, how many times would you expect to pick a ♥?

If you picked one random card from the deck three times, how many times would you expect to pick a ♥?

If you picked one random card from the deck 99 times, how many times would you expect to pick a ♥?