5 marbles are selected from a bag, without replacement. the bag orginally contained 7 red marbles and 9 blue ones. what is the probability that:
1) exactly 3 are red?
2) at least 3 are red?
2007-05-20 18:07:37 · 8 answers · asked by superduper 1 in Science & Mathematics ➔ Mathematics
nobody got it right yet...i have the answer. i just need to know how to get there. show steps plz
2007-05-20 18:27:28 · update #1
You would use combination formula for this.
1. P(exactly 3 are red) = [C(7,3) * C(9,2)] / C(16, 5) = 15/52
2. P(at least 3 are red) means either 3, or 4, or 5 are red, so you calculate each probability and add all three together.
P(3 are red) = [C(7,3) * C(9,2)] / C(16, 5) = 15/52
P(4 are red) = [C(7,4) * C(9,1)] / C(16, 5) = 15/208
P(5 are red) = C(7,5) / C(16, 5) = 1/208
Add all 3 together: 15/52 + 15/208 + 1/208 = 19/52
good luck!
2007-05-20 19:05:47 · answer #1 · answered by birdwoman1 4 · 0⤊ 0⤋
Since the order of the marbles, once extracted from the bag, is immaterial, this is a combination problem. (Ignoring colors, there are 16C5 possible combinations -- a datum not needed for this problem). The probability of 3 reds is (7/16)(6/15)(5/14), and for the second part, add to this the probabilities of 4 red and 5 red.
2007-05-20 18:23:21 · answer #2 · answered by Anonymous · 0⤊ 0⤋
There are 21C5 ways to choose 5 marbles from the 21, using combinations since order doesn't matter. There are 7C3 ways to choose 3 red from among the 7, and 14C2 ways to choose the other 2 from among the 14 nonred.
So for 1) P(3 red) = 7C3 • 14C2 / 21C5 = 0.1565
For 2) add P(3 red) + P(4 red) + P(5 red), computing each P() similarly.
2007-05-20 18:22:22 · answer #3 · answered by Philo 7 · 0⤊ 0⤋
combination
exactly 3 are red = (7/16)*(6/15)*(5/14)*(8/13)
*(7/12)*(5c3)
since there are 5c3 orders in which you can successfully pick exactly 3 red.
at least 3 red is the above + exactly 4 red + exactly 5 red.
exactly 4 red = (7/16)*(6/15)*(5/14)*(4/13)
*(7/12)*(5c4)
exactly 5 red = (7/16)*(6/15)*(5/14)*(4/13)
*(3/12)*(5c5)
2007-05-20 18:21:26 · answer #4 · answered by Bradley B 2 · 0⤊ 0⤋
the probability that three are red is 100% because there are 7 red marbles in the first place.
2007-05-20 18:14:32 · answer #5 · answered by Kilty 5 · 0⤊ 4⤋
1) Pᵣ ( k = 3 ) = 0.288461
2) Pᵣ ( k ≥ 3 ) = 0.365385
2007-05-20 20:26:48 · answer #6 · answered by Zax 3 · 0⤊ 0⤋
exactly 3 are red
(5x7)(4x6)(3x5)(2x9)(1x8) / (16x15x14x13x12)
at least 3 are red.
1 - ( (5x7)(4x6)(3x9)(2x8)(1x7) / (16x15x14x13x12) )
we use combination all the time because. order is not important.
2007-05-20 18:26:31 · answer #7 · answered by Anonymous · 0⤊ 0⤋
probably combination. #2 because there would be more blue than red.
2007-05-20 18:13:30 · answer #8 · answered by cowee88 2 · 0⤊ 4⤋