Respuesta :
Answer:
a. [tex]\frac{3}{8}[/tex]
b. [tex]\frac{7}{52}[/tex]
c. [tex]\frac{95}{156}[/tex]
Step-by-step explanation:
Given,
Total books = 40,
Maths books = 20,
History books = 15,
Geography books = 5,
a. If a book is randomly selected,
Then the probability that the book is a history book,
[tex]=\frac{\text{Ways of choosing history book}}{\text{Ways of choosing any one book}}[/tex]
[tex]=\frac{^{15}C_1}{^{40}C_1}[/tex]
[tex]=\frac{15}{40}[/tex]
[tex]=\frac{3}{8}[/tex]
b. If two book is randomly selected,
Then the probability that both books are from history,
[tex]=\frac{\text{Ways of choosing two history book}}{\text{Ways of choosing any two book}}[/tex]
[tex]=\frac{^{15}C_2}{^{40}C_2}[/tex]
[tex]=\frac{\frac{15!}{2!13!}}{\frac{40!}{2!38!}}[/tex]
[tex]=\frac{105}{780}[/tex]
[tex]=\frac{7}{52}[/tex]
c. If two book is randomly selected,
Ways of selecting any two books from different subjects
= maths and history + maths and geography + history and geography,
[tex]=^{20}C_1\times ^{15}C_1+^{20}C_1\times ^{5}C_1+^{15}C_1\times ^{5}C_1[/tex]
[tex]=20\times 15 + 20\times 5 + 15\times 5[/tex]
[tex]=300 + 100 + 75[/tex]
[tex]=475[/tex]
Then the probability that both books are from different subjects
[tex]=\frac{\text{Ways of selecting any two books from different subjects}}{\text{Ways of choosing any two book}}[/tex]
[tex]=\frac{475}{780}[/tex]
[tex]=\frac{95}{156}[/tex]
