Probability Tes...

$$X$$ has three children in his family. The probability  of one girl and two boys is......

A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing tests I, II and III are respectively $$p,q$$ and $$\cfrac{1}{2}$$. If the probability of the student to be successful is $$\cfrac{1}{2}$$. Then

A car is parked by an owner in a parking lot of $$25$$ cars in a row, including his car not at either end. On his return he finds that exactly $$15$$ placed are still occupied. The probability that both the neighboring places are empty is

Urn $$A$$ contains $$6$$ red and $$4$$ black balls and urn $$B$$ contains $$4$$ red and $$6$$ black balls. One ball is drawn at random from urn $$A$$ and placed in urn $$B$$. Then one ball is drawn at random from urn $$B$$ and placed in urn $$A$$. If one ball is now drawn at random from urn $$A$$, the probability that it is red is

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

Player $$A$$ is more likely to win if

The probabilities that a student will solve Question A and Question B are $$0.4$$ and $$0.5$$ respectively. What is the probability that he solves at least one of the two questions?

It is given that a family of $$3$$ children has two girls, what is the probability that the other child is also a girl?

If $$A$$ and $$B$$ are two events such that $$2P(A)=3P(B)$$, where $$0< P(A)< P(B)< 1$$, then which one of the following is correct?

A number is selected at random from the first $$1,000$$ natural numbers. What is the probability that the number so selected would be a multiple of $$7$$ or $$11$$?