Maths · Statistics and probability · chapter 14 of 14
Class 10 Maths Chapter 14: Probability case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
At a book fair in Kolkata, a publisher's stall runs a lucky dip for children. It seals 120 envelopes, each holding one gift, and puts them in a drum. A child who buys a book draws one envelope at random. The organisers recorded the gifts they sealed, as shown in the table. They now want to know how likely each kind of gift is, so that they can decide how many envelopes of each kind to prepare for the next day.
| Gift | Number of envelopes |
|---|---|
| Bookmark | 54 |
| Pen | 36 |
| Notebook | 24 |
| Book voucher | 6 |
Part 1 · 1 mark
The probability that a child draws a pen is
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Answer: (a) 310
P(pen) = 36/120 = 3/10. 3/7 divides by the 84 envelopes that are not pens.
Part 2 · 1 mark
The probability that a child does not draw a bookmark is
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Answer: (a) 1120
P(bookmark) = 54/120 = 9/20, so P(not a bookmark) = 1 − 9/20 = 11/20.
Part 3 · 2 marks
Find the probability that a child draws a notebook or a book voucher, and verify that the probabilities of the four gifts add to 1.
Answer and marking scheme
Notebook or voucher: 24 + 6 = 30 envelopes, P = 30/120 = 1/4. Sum: 54/120 + 36/120 + 24/120 + 6/120 = 120/120 = 1.
- P(notebook or voucher) = 30/120 = 1/4 (1)
- four probabilities add to 1 (1)
Or
After the first hour, 20 envelopes, all holding bookmarks, have been drawn and not replaced. Find the probability that the next child draws (i) a bookmark, (ii) a book voucher.
Answer and marking scheme
100 envelopes remain, 34 of them bookmarks. (i) P(bookmark) = 34/100 = 17/50. (ii) P(book voucher) = 6/100 = 3/50.
- 100 envelopes, P(bookmark) = 17/50 (1)
- P(book voucher) = 3/50 (1)