Law of Large Numbers
In the long run, a fair coin lands heads about this proportion of the time.
What is 0.50?
A card is drawn from a standard deck. The probability it is a heart or a spade is this decimal.
What is 0.50?
Of a survey of teenagers, 120 have a phone, 130 have a sibling, 75 have both, and 75 have neither. This decimal is the probability of having both a phone and a sibling.
What is 0.30?
A fair coin is flipped twice. The probability of heads both times is this decimal.
What is 0.25?
The probability of rolling a 4 on a fair six-sided die is about this decimal.
What is 0.167?
A fair die shows a 6 five times in 12 rolls. This result alone does not prove the die is unfair because of this.
What is random variation in a small number of trials? Or, what is the law of large numbers?
A fair die is rolled. The probability of rolling a 2 or an odd number is this decimal.
What is 0.67?
Of a survey of teenagers, 120 have a phone, 130 have a sibling, 75 have both, and 75 have neither. This decimal is the probability of having a phone but no sibling.
What is 0.18?
A bag has 4 blue and 6 yellow socks. Two socks are drawn without replacement. The probability both are blue is about this decimal.
What is 0.133?
A fair coin pays $10 for heads and $0 for tails. This is the expected payout.
What is $5?
After four heads in a row on a fair coin, this is the probability of tails on the next toss.
What is 0.50, because the tosses are independent?
Of 40 students, 18 play a sport, 15 play an instrument, and 6 do both. The probability a student plays a sport or an instrument is this decimal.
What is 0.675?
Of a survey of teenagers, 120 have a phone, 130 have a sibling, 75 have both, and 75 have neither. This decimal is the probability of having a phone or a pet.
What is 0.7?
A fair die is rolled, then a fair coin is flipped. The probability of rolling an even number and getting heads is this decimal.
What is 0.25?
A raffle ticket costs $2. There is a 0.01 probability of winning $100 and a 0.99 probability of winning nothing. This is the expected net gain per ticket.
What is -1?
In 600 rolls of a fair die, this is the expected number of 6s.
What is 100?
Two fair dice are rolled. The probability that at least one die shows 6 is about this decimal.
What is 0.306?
Of a survey of teenagers, 120 have a phone, 130 have a sibling, 75 have both, and 75 have neither. Given that a student has a sibling, the probability they also have a phone is about this decimal.
What is 0.577?
A card is drawn from a standard deck and not replaced. The probability the first and second cards are both aces is about this decimal. Assume there are no jokers (52 card deck).
What is 0.0045?
An ad campaign costs $20,000. It has a 0.20 chance of increasing revenue by $70,000, a 0.30 chance of increasing revenue by $30,000, and a 0.50 chance of no increase. This is its expected net value.
What is 3,000?
A fair coin is flipped 1,000 times. The probability of heads is 0.50, but the observed proportion is 0.54. If the coin is flipped another 9,000 times, what proportion of heads would you expect across all 10,000 flips?
What is about 0.504?
If P(A)=0.48 P(B)=0.35, and P(A and B)=0.22, this is P(A or B).
What is 0.61?
Having a phone and having a pet are this type of events.
What are dependent events? (Must prove your answer)
A box contains 5 red and 3 green balls. Two are drawn without replacement. The probability of getting one red and one green, in either order, is about this decimal.
What is 0.536?
The Kings play the Spurs tonight. The Kings are the underdog and have odds of +1000. This means if you bet $100 and they win, you will profit $1000. If you bet $100 on the Kings, what is your expected net gain?
What is 0?