A coin is tossed by students in a simple experiment. Matthew tosses the coin 6 times, Mark 6 times, Luke 6 times, and John 12 times. Imagine you are Matthew, Mark, Luke, and John. Take a coin and reproduce their experiment. What are your results each time? Of the four students, whose experiment would be... Read More

  A student is driven through Dublin and records whether he gets a “red” or “green” light at each set of traffic lights. He records the following outcomes for 10 sets of traffic lights (R represents “red” and G represents “green”): {R, G, R, G, G, G, R, G, G, G}   What is the... Read More

Three children are playing different games. The first child is rolling a fair six-sided die and needs to get a ‘6.’ The second child is flipping a fair coin and needs to get ‘heads.’ The last child is about to spin a wheel and land on the only ‘red’ section, as shown to the left.... Read More

An insurance company is calculating the risk of a fire breaking out in a factory during the next 365 days. It also calculates the risk of a flood damaging the factory. The probability of a fire breaking out is 0.0001, and the probability of a flood occurring is 0.00001. Of the two events, which is... Read More

A student living in Ireland picks a day at random from the calendar. Is it likely or unlikely that the day will have 24 hours? Do not calculate the probability.            

Compute (i.e., simplify into a single term) the following expression, where $k$ and $i$ are nonzero natural numbers:   $$\binom{k}{i-1} + \binom{k}{i}$$  

A researcher has 7 distinct books but wants to place only 5 of them on a shelf (as illustrated in the figure on the left). In how many ways can he arrange these 5 books on the shelf?        

A manager is forming a team of 11 players. She has 20 players in her club to choose from, but there is only one goalkeeper, who must be selected. Therefore, how many different teams can she form?        

A student has 6 distinct books on a bookshelf. These books can be arranged in many ways. One such arrangement is shown in the figure on the left. In how many ways can these books be arranged, assuming all books remain on the shelf, and none are removed?

A customer in a coffee shop can order an Americano, Cappuccino, or Latte. The drink can be either large or small, and it can be either takeaway (to go) or dine-in (stay). How many possible drink orders are there? You do not need to list any of them.