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Question

We give 6 cards to a person and ask him to guess their colors in-order and he knows that a half of cards are black and the other half is white. What is the problality of guessing 5 card's color correctly?(give reasons for your answers)

Answer 1

It depends on if the person has to guess the order of all the cards, then gets to see them all, or if the person guesses them and sees them turned one at a time.

If you want to know what the odds are of the person getting 5, and ONLY five correct, they are zero unless the person is screwing around. Because if you got 5 correct, you got the sixth correct as well.

Answer 2

This is assuming the person has to guess the order before he sees the cards.

In a succession of five cards there can be either 3 white & 2 black or 3 black and 2 white.
In the first possibility the possible combinations of the cards are as follows:
1. wwwbb
2. wwbbw
3. wbbww
4. bbwww
5. wwbwb
6. wbwbw
7. bwbww
8. wbwwb
9. bwwbw
10.bwwwb
So the probability of correctly guessing the order is 1 in 10 = 10%

Similarly in the second possibilty the possible combinations of the cards are as follows:
1. bbbww
2. bbwwb
3. bwwbb
4. wwbbb
5. bbwbw
6. bwbwb
7. wbwbb
8. bwbbw
9. wbbwb
10.wbbbw
So again the probability of correctly guessing the order is 1 in 10 =10%.
The chances of getting either 3 black and 2 white cards or 3 white and 2 black cards are equal, i.e. the chances of getting either one is 1 in 2 =50%. So together, combining the probabilities:

50% x 10% = 5% (0.5 x 0.1 = 0.05)
So the chances of a corrent guess is 1 in 20 = 5%.

Hope I explained that right.

Answer 3

In every part of 5 cards the possibility to guess correctly is 1/2 (3/6) .So the probability is:

1/2*1/2*1/2*1/2*1/2 = 1/32

Additionally,the probability to guess all 5 wrong is the same 1/32,because the card quantities are equal.

Note: My answer is thinking you are putting the cards back.If not then it will change.

Answer 4

The answer is 0. There's no way it can happen.

With 6 cards from which to choose, if a person gets 5 correct, the 6th would have to be known. A person can correctly guess 1, 2, 3, 4, or 6 cards. (If the person misses the first five, the sixth will also be known, so there's no way to get zero correct, either.)

Answer 5

First, the chances of his guessing 5 in a row is the same as his guessing 6 in a row since, after guessing 5, there is only one choice left for the 6'th card

Now......... How many ways can 3 black and 3 white cards be ordered? There is a formula for this but I don't remember it, I'm *not* gonna spend a couple hours digging it out, and, for small values, it's probably quicker to just enumerate them anyway. The algorithm should be obvious.

[bbbwww]
[bbwbww]
[bbwwbw]
[bbwwwb]

[bwbbww]
[bwbwbw]
[bwbwwb]
[bwwbbw]
[bwwbwb]
[bwwwbb]

[wbbbww]
[wbbwbw]
[wbbwwb]
[wbwbbw]
[wbwbwb]
[wbwwbb]

[wwbbbw]
[wwbbwb]
[wwbwbb]
[wwwbbb]

for a total of 20 ways to order 3 black and 3 white cards.

Therefore, the probability of 'guessing' the order of the cards is 1 in 20.


Doug

Answer 6

It depends on the smartness of the person guessing the cards if she always say color black although she knows there are only 3 blacks in it she will have a chance of 1 that she has 3 cards correct. and a chance of 0 that she has 5 cards correct.

Answer 7

If he does smart guessing:

1/2 x 3/5 x 2/4 x 2/3 x 1/2

= (1 x 3 x 2 x 2 x 1)/(2 x 5 x 4 x 3 x 2)

= 12/240

= 0.05

Rationale:
1st guess, any color, chance is 3 out fo 6.
2nd guess, should guess the other color, 3/5, better chance
3rd guess, any color, chance is 2/4
4th guess, again, guess the other color, 2/3
5th guess, guess any color, 1/2

Answer 8

The answer to your question is the same answer as if your question was:

" What is the probability of guessing all of the cards colors correctly."

Because if you guess 5 cards colors correctly then by the time you get to the 6th card your sample space has been reduced to the one color missing, and you must pick it

Now, if you have n objects of which n_1, n_2 ...n_r are indistinguishable then the number of unique permutations is given by:

n!/(n_1! n_2! ... n_r!)

so in this case we have:

6!/(3!3!) = 20

so the probability you guess the correct order of the cards colors is:

1/20

EXTRA: If by your question you are trying to elude to "What is the probability of guessing 5 correctly and 1 incorrectly?", then the only possible answer is 0, because the question would be absurd.

Answer 9

guess three black first and three white second... the chances are 1/6 x 1/6 x 1/6 x 1/6 x 1/6 of getting five correct is 7,776 if the cards are replaced in the deck

Answer 10

This problem is essentially very simple:

Look, the number of favourable ways is the permutation of 6 cards taken 5 at a time, i.e. 6P5. The total number of arrangements is 6! Thus the probability is 6P5/6! = 6/720 = 1/120

So probability is 1 in 120. petewentz4 is the only correct answer together with my answer. Of course I explain it a lot better but then again, pete is in eighth grade.

Answer 11

He has a 3.125% chance of being right.
He has a 50% shot of getting the first card right, and 50% for each consecutive card.

.50^5=.03125

Half being white and half being black is irrelevant because he would not know what ahs already been picked.
If he got to see the card he picked as he picked them his odds would improve dramatically.