Çözüldü Probability - Rational Fractions (8th Grade)

What is the probability that a marble drawn at random from each of two bags—one bag containing 3 white, 7 red, and 15 black marbles, and the other bag containing 10 white, 6 red, and 9 black marbles—will be of the same color?

Solution - 1: (3 / 25)·(10 / 25) + (7 / 25)·(6 / 25) + (15 / 25)·(9 / 25) = 30 / 625 + 42 / 625 + 135 / 625 = 207 / 625.

Solution - 2:

Kod:

1st Bag----------2nd Bag-----------Probability(Two Different Marbles)
White             Red                        3/25·6/25
White             Black                      3/25·9/25
Red               White                      7/25·2/25
Red               Black                      7/25·9/25
Black             White                      15/25·10/25
Black             Red                        15/25·6/25

Probability(Two Same Marbles) = 1 - Probability(Two Different Marbles)
Probability(Two Same Marbles) = 1 - (3/25·6/25 + 3/25·9/25 + 7/25·10/25 + 7/25·9/25 + 15/25·10/25 + 15/25·6/25) = 207 / 625.

https://www.wolframalpha.com/input?...25 + 7/25·9/25 + 15/25·10/25 + 15/25·6/25) =

Source (Turkish): "Introduction to Mathematical Statistics", Prof.Dr. Uğur Korum, Ankara University, Political Sciences Department Press, 1985, Page 47, Question 15