Respuesta :
Answer: The required probability is 65.26%.
Step-by-step explanation: Given that two students form a group of eight boys and 12 girls are sent to represent the school in a parade.
We are to find the probability that the students chosen are not both girls, if the two students are chosen at random.
Total number of students in the group = 8 + 12 = 20.
Let S denote the sample space for the experiment of selecting two students and A denote the event that both the students are not girls.
Then,
[tex]n(S)\\\\=^{20}C_2\\\\\\=\dfrac{20!}{2!(20-2)!}\\\\\\=\dfrac{20\times19\times18!}{2\times1\times18!}\\\\=190,\\\\\\\\n(A)\\\\\\=^8C_2\times^{12}C_0+^8C_1\times^{12}C_1\\\\\\=\dfrac{8!}{2!(8-2)!}\times1+8\times12\\\\\\=28+96\\\\=124.[/tex]
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{124}{190}=\dfrac{62}{95}\times100\%=65.26\%.[/tex]
Thus, the required probability is 65.26%.
