A tennis tournament has n = 64 players, who are drawn uniformly at random to play against each other on the first day of the tournament. Specifically, the draw process is conducted as follows. The 64 names are put in a box, and then drawn at random one-by-one without replacement. The two players whose names are drawn first and second play against each other. The two players whose names are drawn third and fourth play against each other. And so on: players whose names are drawn in positions 2i–1 and 2i, for all i = 1,2,... , 32, play against each other. a. Alice and Bob are among the 64 players. What is the probability that they play against each other on the first day? b. Of the 64 players, k are left-handed and 64 – k are right-handed. For each k = 2,3,...,32, what is the probability that none of the k left-handed players play against each other on the first day?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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