There are 3 first grade children, 5 second grade children, and 6 third grade children in a room. When choosing two children, what is the conditional probability of choosing a second grade child given that either a first or a third grade child was chosen first? (in fraction form)

Suppose you are going to form a committee of students and faculty. You have 7 total students and 12 total faculty to pick from. You want to have 8 total people on the committee. What is the probability that you select 2 students and 6 faculty? Enter your answer rounded to two decimals. Show your work. Enter the work that you used to get your answer.

The table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Sophia’s car over several months. Sophia’s Gas Fill Up LogMiles Driven, x           346    309    336    310    325    274    324Cost to Fill up ($), y    27.69    25.08    25.74    24.56    24.94    22.05    26.28 Step 1 of 2:  Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.

A desk drawer contains: 4 pairs of scissors, 10 paperclips, 5 rubberbands, 6 pens, 8 pencils, and 2 highlighters. You take out two items at random 1. Find the probability of picking two paperclips 2. Find the probability you pick one paperclip and one rubber band  3. Find the probability you pick two rubber bands