Probability

Anahatha wrote:OG 11
Page:182
Problem # :217
(Sorry for not tying the entire question here)

The answer is given as 3/40000.

My doubt : why isn't the answer (3/40000) + (3/40000) since we can first choose a sibling from senior class then junior senior class OR junior class and then senior class.

Can someone please explain ? Thanks in advance..

I have this book:

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students will be a sibling pair.

(I'm too tired to type the options)

You find your answer by use the AND probability formula P(A)*P(B) since the question is asking, "What is the probability that we pick a junior that has a sibling that is a senior, AND then select that person's sibling?"

There are 60 sibling pairs, and there are 1,000 juniors, so the probability of selecting a Junior that is part of a sibling pair is 60/1,000

There are 800 seniors, and only one senior can be the selected junior's sibling, so the probability of making that selection is 1/800

P(A)*P(B) => 60/1,000*1/800 = 3/40,000

As for your question, it does not matter what order you make the random selection. Just as 2*3=6, 3*2=6. You'll always come up with the same number if you remember that the AND probability formula is applied to questions such as these.

Clearly, a sibling pair is a set. i.e. One senior and one junior {s,j}. As long as this is true you will turn up with

60/800 * 1/1000 if the selection is senior first and junior next = 3/40000

(or)

60/1000 * 1/800 if the selection is reversed. Either way, you need only one sibling pair.

Thank you all . Thank you edvhou812 for typing the question

A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?

(1) y ≤ 8
(2) y ≥ 4


Simplifying the question :


The probability of obtaining one red marble and one white marble is given by:

P(Red AND White) =
[8/8 + y] ×[ y/7 + y] × 2 = 16y/[(8 + y) × (7 + y)]

Note the multiplier of 2 in the second expression. That is because there are TWO different ways Joan could obtain a Red and a White marble if Joan pulls out two marbles sequentially:

Red THEN White
White THEN Red

MY DOUBT : HOW IS THIS DIFFERENT FROM THE PREVIOUS PROBLEM I POSTED ? PLEASE EXPLAIN WHY DO WE NEED TO MULTIPLY BY 2?