June 2021

A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is 1/2. How small can the number of socks in the drawer be?

In a certain municipality, all seven-digit telephone numbers begin with 321. How many telephone numbers maybe assigned to that municipality if the last four digits should not begin or end in zero?

A cat takes 4 leaps to a dog's 3; but 2 of the dog's leaps are equivalent to 3 of the cat’s. The cat has a start of 50 leaps. How many leaps must the dog take to catch the cat?

An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle a circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on indefinitely. Find the sum of the areas of all the triangles.

A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. Suppose that the retailer receives 10 shipments in a month and the inspector randomly tests 20 devices per shipment. What is the probability that there will be 3 shipments containing at least one defective device?

The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that at least 10 survive?

The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive.

The number of cars passing a point on a road during a five-minute period may be modelled by the Poisson distribution with parameter 4. Find the probability that in five-minute period, fewer than 3 cars go past.

Suppose a population is normally distributed with a mean of 24.6 and a standard deviation of 1.3. What percentage of data will lie between 25.3 and 26.8?