Math Challenge 2?

Question

If you could help me thanks...also tell and show me how tou did it.

2. A jar contains 2 blue marbles and 4 green marbles. Without looking two marbles are drawn from the jar. What is the probability that both marbles are the same color? Express your answer as a percent and round to the nearst tenth.Note:After a marble is drawn it is not put back. Thanks sooooooo much if you solve it... it really will help me !!!!

Answer 1

There are 2 blue marbles and 4 green marbles...
No of ways you can drwar 2 blue marbles = 2C2 = 2 * 1/( ( 2* 1) * 0!) = 1 (using the formula n C r = n! / ((n-r) ! *r!) and since 0! = 1 Hence the result.
No. of ways you can draw 2 green marbles = 4C2 = 4! / ((4 - 2)! * 2!) = 4!/(2!* 2!) = ( 4 * 3* 2* 1)/((2* 1) * ( 2* 1)) = 6
Therefore, the total no of ways you can draw 2 balls of the same colour = 1+ 6 = 7 ways

Now, Total no. of ways you can draw *2 balls out of 6 balls = 6C2 =6!/((6-2)!*2!) = (6*5*4*3*2*1)/((4*3*2*1) * (2*1)) = 15 ways

Therefore, The no of ways you can draw 2 balls of the same colour from the total of 6 balls of the types aforementioned = 7/15 = 7/15 * 100 = 140/3 % = 46.67%

Answer 2

2 blue and 4 green = 6 total

odds for both blue drawn are as follows
there are 2 blue out of 6 total, that is a 1 in three chance 1/3
after it is drawn there is 1 blue of 5 total a chance of 1 in 5 1/5
you get the probability of this happening by multiplying 1/3 by 1/5 which is 1/15

do this the same for green
i will only show the numbers
4/6 = 2/3
3/5 remain
2/3 x 3/5 = 6/15 (the possibility of both being green)

Answer 3

Okay, theres (4+2) marbles in all.
That means theres 6*5 = 30 total possiblilities.

Now with blue marbles, theres 2*1 = 2 possiblities to get 2 marbles that are both blue.
And with green, there are 4*3=12 possbilities to get 2 marbles that are both green.

So, probability is (2+12)/30 = 14/30 = 46.666..% approximately.

Answer 4

marble 1 can be either blue or green (doesn't matter)
for the second marble there are 2 options:

20% chance its a blue one (agian) (1 remaining blue vs. 4 remaining green = 1/5)
60% chance its a green one (agian) (3 remaining green vs 2 remaining blue = 3/5)

20+60=80/2= 40% chance to draw 2 marbles of the same colour.

Answer 5

Thera are 6*5/2 = 15 pairs. Obviously there are 4*2 pairs of different colors, so 7 pairs of the same colour. So P = 7/15 =46,7%