Class 10 Maths Chapter 14 Probability Extra Questions (HOTS)

Genuinely harder, HOTS-level practice for Class 10 Maths Chapter 14 (Probability), going beyond the textbook exercise with fresh scenarios and reverse-engineering problems. These Class 10 Mathematics Chapter 14 important questions are handy for last-minute exam practice.

1. Q1 (Assertion-Reason). Assertion (A): P(sum=13 on two dice)=0. Reason (R): P(impossible event)=0 always.
   Solution: Max sum on two dice is 6+6=12, so sum=13 is impossible, confirming A. R correctly states the general rule and explains A. Answer: Both A and R true, R explains A.
2. Q2 (Reverse-engineering). A bag has some red marbles and 18 green marbles. P(red)=2/5. Find the number of red marbles and total marbles.
   Solution: r/(r+18)=2/5 ⇒ 5r=2r+36 ⇒ r=12. Total=30 (12 red, 18 green). Check: 12/30=2/5 ✓
3. Q3 (Fresh scenario). Two dice thrown together. Find P(product of the two numbers is a perfect square).
   Solution: Total=36. Products that are perfect squares (1,4,9,16,25,36): (1,1)=1 way; (1,4)(4,1)(2,2)=3 ways for 4; (3,3)=1 for 9; (4,4)=1 for 16; (5,5)=1 for 25; (6,6)=1 for 36. Total favourable=8. P=8/36=2/9.
4. Q4 (Fresh scenario). A card drawn from 52. Find P(neither a king nor a queen).
   Solution: Exclude 4 kings+4 queens=8. Favourable=52-8=44. P=44/52=11/13.
5. Q5 (Fresh scenario). Four fair coins tossed together. Find P(exactly 2 heads), P(at least 3 heads), P(no head).
   Solution: Total=2⁴=16. Exactly 2 heads=⁴C₂=6 ⇒ 3/8. At least 3=4(exactly 3)+1(exactly4)=5 ⇒ 5/16. No head=1 (TTTT) ⇒ 1/16.
6. Q6 (Reverse-engineering with follow-up). A box has some red pens and 15 blue pens. P(red)=3/8. Find red pens and total. If 5 more blue pens are added, find the new P(red).
   Solution: r/(r+15)=3/8 ⇒ 8r=3r+45 ⇒ r=9. Total=24 (9 red, 15 blue). After adding 5 blue: total=29, red unchanged=9. New P(red)=9/29.
7. Q7 (Fresh scenario). Two dice thrown together. Find P(sum is a multiple of 4).
   Solution: Multiples of 4 possible: 4,8,12. Sum4=3 ways, Sum8=5 ways, Sum12=1 way. Total favourable=9. P=9/36=1/4.
8. Q8 (Fresh scenario). A letter is chosen at random from the word MATHEMATICS. Find P(vowel), P(letter is M), P(consonant).
   Solution: 11 letters: M=2,A=2,T=2,H=1,E=1,I=1,C=1,S=1. Vowels(A,E,I)=2+1+1=4 ⇒ P(vowel)=4/11. P(M)=2/11. Consonants=11-4=7 ⇒ P(consonant)=7/11.

More on This Chapter

• NCERT Solutions – Chapter 14
• Extra Questions (HOTS) – Chapter 14
• Revision Notes – Chapter 14
• Class 10 Maths Book (Catalog Page)

Written by Satish

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