Probability Tes...

$$10$$ mangoes are to be distributed among $$5$$ persons. The probability that at least one of them will receive none is :

Which of the following is true regarding law of total probability?

From $$30$$ bulbs out of which $$10$$ are defective, $$3$$ bulbs are chosen. X denotes number of defective bulbs.The PDF of r.v x is

A bag contains three red balls and two blue balls. We remove successively, and with replacement, two balls and observe their colour. What is the probability of "to extract a red ball and a blue one, without taking into account the order"?

One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9 black balls. One ball is taken from each bag. What is the probability that both the balls will be of the same colour?

I have three bags that each contain $$100$$ marbles- Bag $$1$$ has $$75$$ red and $$25$$ blue marbles, Bag $$2$$ has $$60$$ red and $$40$$ blue marbles, Bag $$3$$ has $$45$$ red and $$55$$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?

We draw two cards from a deck of shuffled cards without replacement. Find the probability of getting the second card a queen.

At a certain university, $$4$$% of men are over $$6$$ feet tall and $$1$$% of women are over 6 feet tall. The total student population is divided in the ratio $$3:2$$ in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman?

Two coins are tossed. Find the conditional probability that two Heads will occur given that at least one occurs.

From a batch of $$100$$ items of which $$20$$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probabilities that the second item chosen is defective.