In large cupboard of books consisting of 8 books on mathematics, 10 books on Geography, 3 on Economics and 5 books on Statistics. four books are chosen for study purpose. What is the probability that a) Only Statistics books will be chosen? b) There will be 3 Economics books chosen for study? c) All subjects are represented d) Only Statistics and Economics books will be chosen? e) None of Statistics book will be chosen?
Answers
Given : In large cupboard of books consisting of 8 books on mathematics, 10 books on Geography, 3 on Economics and 5 books on Statistics. four books are chosen for study purpose.
To find : probability that a) Only Statistics books will be chosen? b) There will be 3 Economics books chosen for study? c) All subjects are represented d) Only Statistics and Economics books will be chosen? e) None of Statistics book will be chosen?
Solution:
Mathematics = 8
Geography = 10
Economics = 3
Statistics = 5
Total = 26
. four books are chosen for study purpose
number of ways = ²⁶C₄ = 14950
Only Statistics books will be chosen
Number of Ways = ⁵C₄ = 5
Probability Only Statistics books will be chosen = 5/14950 = 1/2990
There will be 3 Economics books chosen for study
Number of ways = ³C₃ * ²³C₁ = 23
Probability 3 Economics books chosen for study = 23/14950 = 1/650
All subjects are represented
Number of ways = ⁸C₁ * ¹⁰C₁ * ⁵C₁ * ³C₁ = 8 * 10 * 5 * 3 = 1200
Probability All subjects are represented = 1200/14950 = 24/299
d) Only Statistics and Economics books will be chosen?
Number of ways = ⁽³⁺⁵⁾C₄ = ⁸C₄ = 70
Probability Only Statistics and Economics books will be chosen = 70/14950
= 7/1495
e) None of Statistics book will be chosen?
Number of Ways = ⁽²⁶⁻⁵⁾C₄ = ²¹C₄ = 5985
probability None of Statistics book will be chosen = 5985/14950
= 1197/2990
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