Probability help (Inclusive)

Test Preparation SAT Preparation
1

<p>I need help with these type of "Inclusive Events" probability questions. For example:</p>

<p>A student is selected at random from a group of 12 male and 12 female students. There are 3 male students and 3 female students from each of 9th, 10th, 11th, and 12th grades. Find each probability.</p>

<p>2) P(10th grader OR female)</p>

<p>I know you start off with 6/24 + 12/24 but can someone explain to me WHERE you get the 3/24 and WHY you have to subtract it from 6/24 + 12/24? That's the part I need desperate help with. So the probability of selecting a 10th grader is obviously 6 students and the probability of selecting a female is 12 students. So 6/24 + 12/24. But my teacher said it's not just "6/24 + 12/24" ... he said it's "6/24 + 12/24 - 3/24" .... where the heck do you get the 3/24 from, I'm soooo confused</p>

2

<p>6/24 + 12/24 adds the probabilities of being a 10th grader or female, but you subtract 3/24 to remove the overlap of being a 10th grade female, since in just adding those values, you’re adding 10th grade females twice.</p>

3

<p>^i still don’t understand why you take 3/24 away. like, mathematically, how do you get 3/24? what do you do</p>

4

<p>^ The rule of P (A or B) is always P(A) + P(B) - P(A and B). The A and B produces a repetition of an already existing group, which is why you need to take it out.</p>