Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. On e of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads?

In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to $${25^ \circ }$$ C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above $${25^ \circ }$$ C, or at/below $${25^ \circ }$$ C. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above $${25^ \circ }$$ C?

A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is

Let $$f(x)$$ be the continuous probability density function of a random variable X. The probability that $$a\, < \,X\, \le \,b$$, is: