In this section, you'll find interesting math problems which you
can try to work out yourself before looking at the detailed solutions
I've provided.
Note: I haven't provided solutions to some problems yet; they
will be forthcoming.
Problems on probability:
In answering these questions, make sure you state your assumptions.
And challenge those assumptions. If you find those assumptions
are incorrect or flawed, then try to solve those problems accounting
for those flaws. Look deeper.
 Card probabilities:
 If I pick two cards out of a standard 52card deck, what's the
probability that they are the same suit?
 If I pick five cards out of a standard 52card deck, what's the
probability that I have a royal flush in poker?
 If I pick five cards out of a standard 52card deck, what's the
probability that I have a straight flush (but not anything better)?
 ... 4 of a kind?
 ... a full house (but not anything better)?
 ... 3 of a kind (but not anything better)?
 ... two pair (but not anything better)?
 ... a pair (but not anything better)? Solution
 ... a straight (but not anything better)?
 ... a flush (but not anything better)?
 Birthday probabilities:
 If I pick a person completely at random, what's the probability
that this person has the same birthday as me?
 If I pick 30 people completely at random, what's the probability
that at least one of them has the same birthday as me?
 What's the probability that, out of 30 random people, at least
two of them share the same birthday?
 Other probabilities:
 If I have two kids, what's the probability that they are the same
sex?
 What's the probability of winning the jackpot of the California
lottery? Note, to win the jackpot you must pick 5 numbers from
147, and then pick a MEGA number from 127. All 5 numbers must
match the numbers chosen, and the MEGA number must match the MEGA
number chosen. Solution
 The jackpot for the California lottery is $100 million today.
If I buy 1 ticket, what's my expected value? (only taking into
account the jackpot prize, and not other possible winnings) Solution
 The jackpot for the California lottery is $100 million today.
How many tickets should I buy to maximize my expected value? (only
taking into account the jackpot prize, and not other possible
winnings)
 How high does the jackpot have to go before it becomes statistically
good for me to enter the lottery? (only taking into account the
jackpot prize, and not other possible winnings)
