Random Probability

A color-blind toddler can identify six colors (red, blue, yellow, green, orange, violet, black and white). For an exam, his teacher randomly selected 5 out of 10 colors. What is the probability that the student can identify all 5 colors?

What do you think it is?
I don't mind helping you with your homework, but do mind doing it for you.

My answer is (6C5 * 4C0) / 10C5 = 1/42. I don't know if this is correct or not.

Even though this appears to be someone's homework problem... I'll oblige.

Simple probability. If they can identify 6 colors and there are 10 total colors, this is a conditional probability problem as getting them ALL correct is dependent on getting the first one correct, and then the second one correct, and then the third one correct, etc.

Since they can identify 6 of the 10 colors, the odds of correctly choosing color #1 is 6/10
After the first color is removed, the odds of picking the next color is 5/9
Next is 4/8
Next is 3/7
Next is 2/6

Simply multiply 6*5*4*3*2 and then divide that sum by 10*9*8*7*6 and you will have your probability as a decimal. From my computer calculator, it looks like it comes out to .0476, or 4.76%.

Good luck on your probability exam.

I think you forgot to consider the teacher chooses 5 random colors part? The answer you provided looks like an answer for a sequence-type problem.

Off-topic
Got scared a bit from your name at first, and yeah thanks for the reply.

Quote: gustagaducks

My answer is (6C5 * 4C0) / 10C5 = 1/42. I don't know if this is correct or not.

That's my answer, too. =combin(6,5)*combin(4,0)/combin(10,5)

Duckmankilla got 6*5*4*3*2/(10*9*8*7*6), which is the same answer, although it doesn't equal 4.76%.

I think the problem should have been reworded as: A color-blind toddler can identify six colors (red, blue, yellow, green, orange, and violet) and also black and white... to avoid confusing the math students with the meaning of "colors."

I think your initial guess was right, 1 in 42. This problem makes use of the hypergeometric distribution.

In Excel: hypgeomdist(a,b,c,d) = the probability of matching a out of b, given that c are randomly chosen from d.

Therefore, matching 5 out of 6 identifiable colors, given that 5 are randomly chosen from 10 = hypgeomdist(5,6,5,10) = 1/42 = 0.0238 = 2.38%

Quote: gustagaducks

A color-blind toddler can identify six colors (red, blue, yellow, green, orange, violet, black and white). For an exam, his teacher randomly selected 5 out of 10 colors. What is the probability that the student can identify all 5 colors?

The problem doesn't specify that the 10 color "pool" contains any of the six that the color-blind toddler can identify. My big box of crayons has 128 colors. Perhaps the possibility of zero, needs to be factored in with more weight?

This is clearly a high school or college probability problem... I don't think its getting that complicated. Also, apologies for the incorrect figure before. As i said, I just quickly typed it into the microsoft accessories calculator, so i easily could have made an error there.

Quote: gustagaducks

I think you forgot to consider the teacher chooses 5 random colors part? The answer you provided looks like an answer for a sequence-type problem.

Off-topic
Got scared a bit from your name at first, and yeah thanks for the reply.

The 5 random colors just means that you dont need the last one, which is why i stopped at 2/6. After correctly identifying the first 4, the toddler has a pool of 6 colors remaining and knows 2 of them. It doesn't matter which of the two appears, just that one of the two does.

I'm not the greatest in math formulas, proofs, or things of the sort, but I like to think that I know enough to get by. I never really took to the "conventional approach" of formulas and things that teachers tried to force down my throat, I just like to look at the numbers and see what is logical. Once that happens, the formulas make more sense to me.

As far as the name, it was my original username for the playstation network when it came out. Since I use it for that, I decided to use it for most everything just for convenience purposes. Just makes like easier. No malice towards ducks, as a matter of fact I find them enjoyable to be around.