Question

Two students form a group of eight boys and 12 girls are sent to represent the school in a parade. If the two students are chosen at random, what is the probability that the students chosen are not both girls?

Answer 1

Your best option would be 33/95 hope this helps

Answer 2

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,

$n(S)\\\\=^{20}C_2\\\\\\=\dfrac{20!}{2!(20-2)!}\\\\\\=\dfrac{20\times19\times18!}{2\times1\times18!}\\\\=190,\\\\\\\\n(A)\\\\\\=^8C_2\times^{12}C_0+^8C_1\times^{12}C_1\\\\\\=\dfrac{8!}{2!(8-2)!}\times1+8\times12\\\\\\=28+96\\\\=124.$

Therefore, the probability of event A is given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{124}{190}=\dfrac{62}{95}\times100\%=65.26\%.$

Thus, the required probability is 65.26%.