Respuesta :
Answer:
(a) Probability that the dictionary is selected = 0.1818
(b) Probability that 1 novel and 1 book of poems are selected = 0.3818
Step-by-step explanation:
We are given that 2 books are picked at random from a shelf containing 7 novels, 3 books of poems, and a dictionary.
(a) Probability that the dictionary is selected is given by;
Number of ways of selecting a dictionary from total of 1 dictionary from the shelf = [tex]^{1}C_1[/tex] = 1
Now, since two books are picked from the shelf from which one is dictionary so another book will be from total 10 books (7 novels + 3 poems), so number of ways for doing this = [tex]^{10}C_1[/tex] = 10
Number of ways of selecting total 2 books from total of 11 books from the shelf = [tex]^{11}C_2[/tex] = 55
So, required probability = [tex]\frac{^{1}C_1*^{10}C_1}{^{11}C_2}[/tex] = [tex]\frac{1*10}{55}[/tex] = 0.1818
(b) Number of ways of selecting 1 novel from total of 7 novels from the shelf = [tex]^{7}C_1[/tex] = 7
Number of ways of selecting 1 book of poem from total of 3 books of poems from the shelf = [tex]^{3}C_1[/tex] = 3
Number of ways of selecting total 2 books from total of 11 books from the shelf = [tex]^{11}C_2[/tex] = 55
So, probability that 1 novel and 1 book of poems are selected = [tex]\frac{^{7}C_1*^{3}C_1}{^{11}C_2}[/tex]
= [tex]\frac{7*3}{55}[/tex] = 21/55 = 0.3818
