Mathematics Hothouse

This refers to the previous blog on probability conceptual questions for IITJEE Math.

Hints:

1. The pin may land point up or down. Do you think these cases are equally likely?
2. This is the same as if we tossed two coins once. Then, the outcome is a pair where a and b may be tails or heads.
3. Assuming that the die is regular (fair), we have six equally likely outcomes/ For two dice, an outcome is a pair , where a is the number shown on the first die and b on the second.
4. Again, we have pairs here, but we have to be careful, since the meaning and the range of a and b are different.
5. In this example, there are many possibilities. We may want to know whether mug breaks or not, into how many pieces, which side up it lands (if in one piece).
6. The description of the experiment is not precise. We can draw two cards at once or draw one, return it to the pack, and draw again.
7. The result can be written as a sequence of six numbers.
8. What is the maximum length of the match? How many games may be played?
9. Is there a number N such that in N throws we shall certainly have heads up?
10. We need to choose the scale and then decide what accuracy is possible.
11. Is this a bus stop in the first place (in some cities they have trams)? Does the bus have a time table?
12. Do we include the possibility that it will never arrive?
13. In the extreme case, each letter on the page you consider may be a misprint. (We certainly hope it is not so). Thus, there are at most finitely many misprints.
14. The number of accidents is not necessarily limited by the number of vehicles in the city. A vehicle may be involved in more than one accident on the same day.
15. Depends on the type of display and the individual working habits.

Now, you can try the solutions.

Auf wiedersehen,

Nalin Pithwa