Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.

A purse contains 3 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled out at random from one of the two purses, what is the probability that it is a silver coin?

for a loaded die, the probabilities of outcomes are given as under
P(1) = P(2) = \(\frac { 2 }{ 10 } \), P(3) = P(5) = P(6) = \(\frac { 1 }{ 10 } \) and P(4) = \(\frac { 3 }{ 10 } \)
The die is thrown 2 times. Let A and B be the events as defined below
A: Getting same number each time
B: Getting a total score of 10 or more
Discuss the independency of the events A and B

Out of 10 outstanding students in a school there are 6 girls and 4 boys. A team of 4 students is selected at random for a quiz programme. Find the probability that there are atleast two girls.

In a factory, Machine-I produces 45% of the output and Machine-II produces 55% of the output. On the average 10% items produced by I and 5% of the items produced by II are defective. An item is drawn at random from a day's output. (i) Find the probability that it is a defective item (ii) If it is defective, what is the probability that it was produced by Machine-II?