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# Common Mistakes to Avoid in ICSE Class 10 Board Exams - Chapter Probability

Probability, a chapter from the unit Statistics in the ICSE Class 10 syllabus, contains quite interesting questions. In this chapter, there is very little chance of making calculation errors as calculations are simpler. Yet, mistakes are seen as students fail to understand the event of which probability is to be found and hence, make errors in writing favourable outcomes and hence get the incorrect probability. Let us understand the mistakes committed by students while attempting probability questions.

Mistake in not writing the answer in the SIMPLEST FORM

Despite understanding the question correctly, writing the proper favourable outcomes and calculating the probability correctly, students lose marks for not writing the final answer in the simplest form.

Remember, it is very essential to write the final answer in the simplest form.

Mistakes in attempting questions based on a DECK of 52 cards

There is a lot of confusion among students in understanding a DECK of 52 cards such as how many face cards a deck has? how many suits are there? Which are black colour suits and which are red?

For clear understanding of all these points, one should memorise the following information:

• There are 4 suits Clubs, Spades, Hearts, Diamonds, each containing 13 cards.
• 3 Face cards in each suit – King, Queen, Jack – Total 12 Face cards.
• Black colour cards – Clubs, Spades, Red colour cards – Hearts, Diamonds.

If you remember all the above information properly, the probability of committing mistakes while solving questions on a deck of cards will be zero.

Mistakes in finding probability for ‘less than’, ‘greater than’, ‘at least’, ‘at most’, ‘less than or equal to’, ‘greater than or equal to’ and ‘between’

There are multiple terms involved in probabilities wherein students get confused and because of wrong understanding of these terms, they make mistakes.

Let us understand the meaning of these terms and avoid making errors.

Consider the following question:

Question:

A box contains tickets numbered 1 to 20. A ticket is drawn at random.

Find the probability of drawing a ticket bearing number less than 5.

Less than 5

Here, ticket bearing number 5 is not included but tickets with numbers less than 5 are included. So, tickets bearing numbers 1 to 4 are included.

Find the probability of drawing a ticket bearing number greater than 5.

Greater than 5

Here, ticket bearing number 5 is not included but tickets with numbers greater than 5 are included. So, tickets bearing numbers 6 to 20 are included.

Find the probability of drawing a ticket bearing number at least 5 / greater than or equal to 5.

At least 5 means minimum 5 or more than 5.

Also, greater than or equal to 5 means minimum 5 or more than 5.

Hence, it is very important to understand that at least and greater than or equal to are one and the same. Do not treat them as two different events.

Find the probability of drawing a ticket bearing number at most 5 / less than or equal to 5.

At most 5 means maximum 5 or less than 5.

Also, less than or equal to 5 means maximum 5 or less than 5.

That means, at most and less than or equal to are one and the same and NOT different events.

Find the probability of drawing a ticket bearing a number between 5 and 10.

When an event is between 5 and 10, it should be noticed that 5 and 10 are not included here. The numbers which lie between 5 and 10 are included in this event.

CONCLUSION

The foremost thing to take care in the probability chapter is to read and understand the question clearly and draw favourable outcomes for the asked event. Then, there will be null chances of committing mistakes as the solutions do not have complicated or lengthy calculations. These mistakes are based on CISCE Pupil Analysis done in a year. A huge amount of quality resources is available at TopperLearning for your understanding such as Revision Note explaining all terms of a probability, Assertion and Reasoning Questions and also YT short explaining less than, greater than concept.

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