There are 15 marbles in a bag; 7 of them are red, the other 8 are not red. 4 marbles are drawn WITHOUT replacement.
What is the probability that you'll draw:
1) 0 red
2) 1 red
3) 2 red
4) 3 red
5) 4 red
Thanks in advance for any help :)
0 red: 8/15 * 7/14 * 6/13 * 5/12 = 2/39
1 red: one way would be R, NR, NR, NR (R = red, NR = not red)
= 7/15 * 8/14 * 7/13 * 6/12 =14/195
BUT, the above can be arranged in 4 ways, so prob (1 red) = 56/195
2 red: could be R, R, NR, NR
= 7/15 * 6/14 * 8/13 * 7/12 = 14/195
this can be arranged in 4!/(2!2!) or 6 ways, so prob (2 red) = 28/65
3 red: could be R,R,R,NR
= 7/15 * 6/14 * 5/13 * 8/12 = 2/39
arranged in 4 ways, so prob(3red) = 8/39
4 red: = 7/15 * 6/14 * 5/13 * 4/12 = 1/39
notice: 2/39 + 56/195 + 28/65 + 8/39 + 1/39
= 10/195 + 56/195 + 84/195 + 40/195 + 5/195
= (10 + 56 + 84 + 40 + 5)/195 = 195/195 = 1 , yeahhhh
my answers are correct
Awesome. Thanks so much for your help!
It's funny actually, because I had the same logic, same numbers, but I realized I made a silly calculator error!
To find the probability of drawing a certain number of red marbles, we need to use the concept of combinations.
The total number of ways to choose 4 marbles from 15 is given by the combination formula:
C(n,r) = n! / (r!(n-r)!)
Where n is the total number of objects (15 marbles) and r is the number of objects chosen (4 marbles).
Now, let's calculate the probability for each case:
1) Probability of drawing 0 red marbles:
To calculate this, we need to find the number of ways to choose 4 marbles without any red marbles. Since there are 8 non-red marbles, the number of ways to choose 4 non-red marbles out of 8 is C(8,4). The total number of ways to choose 4 marbles out of 15 is C(15,4). Therefore, the probability is:
P(0 red) = C(8,4) / C(15,4)
2) Probability of drawing 1 red marble:
Similarly, the number of ways to choose 1 red marble out of 7 and 3 non-red marbles out of 8 is C(7,1) * C(8,3). The total number of ways to choose 4 marbles out of 15 is C(15,4). Therefore, the probability is:
P(1 red) = C(7,1) * C(8,3) / C(15,4)
3) Probability of drawing 2 red marbles:
Similarly, the number of ways to choose 2 red marbles out of 7 and 2 non-red marbles out of 8 is C(7,2) * C(8,2). The total number of ways to choose 4 marbles out of 15 is C(15,4). Therefore, the probability is:
P(2 red) = C(7,2) * C(8,2) / C(15,4)
4) Probability of drawing 3 red marbles:
Similarly, the number of ways to choose 3 red marbles out of 7 and 1 non-red marble out of 8 is C(7,3) * C(8,1). The total number of ways to choose 4 marbles out of 15 is C(15,4). Therefore, the probability is:
P(3 red) = C(7,3) * C(8,1) / C(15,4)
5) Probability of drawing 4 red marbles:
Similarly, the number of ways to choose 4 red marbles out of 7 is C(7,4). The total number of ways to choose 4 marbles out of 15 is C(15,4). Therefore, the probability is:
P(4 red) = C(7,4) / C(15,4)
Now, you can use a calculator or a software that can perform factorials and combinations to calculate each probability.