Question

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

Answer 1

Answer: The probability of selecting at least one boy (the probability that the 2 students selected are not both girls) is 62/95 or 0.6526

Step-by-step explanation:

From the question, the students to be chosen must be selected from a group of eight boys and twelve girls. This means that the total number of students that these two students must be chosen from is:

8 + 12 = 20 students.

The next step would be to find the probability of selecting a boy:

= Total number of boys/Total number of students

= 8/20

We will also find the probability of selecting one girl from the group

= Total number of girls/Total number of students

= 12/20

To find the probability that the two selected students are not girls is the same as finding the probability of selecting at least one boy. To do this, we will first find the probability of choosing all girls and then subtract it from 1.

The probability of selecting or choosing 2 girls (without replacement)

(12/20) × (11/19)

= 132/380

= 33/95

Then, the probability of selecting at least one boy (the probability that the students chosen are not both girls)

= 1 - (33/95)

= (95/95) - (33/95)

= 62/95 or 0.6526