Question 59 Answer and Explanation _ACT June 2021 Form D06 Math Section

59. The table indicates the grade (10 or 11) and high school (North or South) of the 270 students enrolled in Algebra II in the Green City School District.

Suppose 2 of these students will be chosen at random to represent the Algebra II classes at a local STEM (Science, Technology, Engineering, and Mathematics) event. Which of the following expressions gives the probability that both chosen students will be from the same grade and the same high school?

A. $\frac{47(46)}{270(269)}+\frac{93(92)}{270(269)}+\frac{73(72)}{270(269)}+\frac{57(56)}{270(269)}$

B. $\frac{1}{4}(\frac{47}{270}+\frac{93}{270}+\frac{73}{270}+\frac{56}{270})$

C. $\frac{47(73)}{270(269)}+\frac{93(57)}{270(269)}$

D. $\frac{47(93)}{270(269)}+\frac{73(57)}{270(269)}$

E. $\frac{1}{4}(\frac{1}{4})$

Answer and Explanation

Your Answer is

Correct Answer is A

Explanation

Taking the probability of North High School in Grade 10 as an example, P=number of selected people/total number of people, the probability of the first person is 47/270, and the total number of people and the number of samples for the second person are one less, that is, 46/269. P=47×46/270×269

The probability of the same grade and the same high school is the sum of 4 cases