An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is

A box contains twelve balls of which 4 are red, 5 are green and 3 are white. If three balls are drawn at random simultaneously from the box, then the probability that exactly 2 balls have the same colour is

There are three families $F_1, F_2, F_3 . F_1$ has 2 boys and 1 girl; $F_2$ has 1 boy and 2 girls; $F_3$ has 1 boy and 1 girl. A family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus selected is a girl, then the probability that she is form $F_2$ is

An urn $A$ contains 4 white and 1 black ball; urn $B$ contains 3 white and 2 black balls and urn $C$ contains 2 white and 3 black balls. One ball is transferred randomly from $A$ to $B$; later one ball is transferred randomly from $B$ to $C$. Finally, if a ball is drawn randomly from $C$, then the probability that it is a black ball is