Practice: Week 0 : Assignment 0

Suppose the probability of two events A and B in a probability space is 0.3 and 0.6 respectively. What is the maximum possible probability for the event A ∩ B?

Suppose the probability of two independent events A and B in a probability space is 0.3 and 0.4 respectively. What is the probability for the event A ∩ B?

Suppose in a factory there are two machines, namely A and B, which produce the same good. The machine A produces 10% of the goods whereas the machine B produces the remaining 90% of the goods. Among the goods produced by machine A, 20% are found to be defective whereas, among the goods produced by machine B, only 10% are defective. For a defective good, what is the probability that it is produced by machine A?

Which of the following is correct?

Which one of the following sorting algorithms have the minimum worst case asymptotic time complexity?

Which algorithm design paradigm the Kruskal’s algorithm for finding a minimum weight spanning tree follows?

In how many ways, 10 identical balls can be distributed among 6 children?

In how many ways, 3 different balls can be distributed among 5 children?

On a set of 20 elements, how many binary relations can be defined?

Solve the following recurrence relation. T ( n ) = { T ( n 2 ) + T ( n 3 ) + 7 n if n ≥ 100 1 otherwise