Kevin's Math Page

# Math Problems

 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 52-card deck, what's the probability that they are the same suit? If I pick five cards out of a standard 52-card deck, what's the probability that I have a royal flush in poker? If I pick five cards out of a standard 52-card 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 1-47, and then pick a MEGA number from 1-27. 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)

Kevin's Math Page