Question

In a large bag of skittles , each of the five (red, orange,yellow,blue,green) occurs with the same probability .you reach in select 2 candies
Find the probability that exactly one of the candies is orange ?

Answer 1

Since the bag has 5 colors (red orange yellow blue and green) it has a denominator of 5 yes?

Answer 2

yes

Answer 3

And we're saying if we pick two, and only one of them is a certain color

Answer 4

If we were picking 1 then it would be 1/5 but we're picking 2, how do we account for that?

Answer 5

since you have 5 different colors and 5 of each color, you have 25 skittles in a bag.

Answer 6

Is it more or less likely?

Answer 7

5/25=1/5...

Answer 8

@anna113 is it more or less likely if we pick 2 instead of 1?

Answer 9

im not sure i guess more likely ??? @LearningIsAwesome

Answer 10

im not good in probabilities

Answer 11

Well we're adding another condition, the condition that we don't pick two of the same color

Answer 12

is it 2/5 @LearningIsAwesome

Answer 13

That would mean it's more likely to happen, remember we're not only saying it's a 1/5 chance, but also it we cannot pick it twice

Answer 14

confused @LearningIsAwesome

Answer 15

Okay, so the higher your numerator is the higher the probability right? cause 1/5=20% and 2/5=40% yes?

Answer 16

yes

Answer 17

And here we could be saying we're going to pick just one, and that'd be 5/25=1/5=20% right?

Answer 18

yes

Answer 19

We also could say the probability of just getting that color when picking twice, one or two, and the probability would go up to be 2/5=40% cause we're picking twice right?

Answer 20

yea

Answer 21

but we're not saying those things, we're saying we will pick twice(driving up the probability) but it HAS to be only one(driving down the probability) makes sense?

Answer 22

yes

Answer 23

Given that each of the five colors have equal probabilty so each has probability
P(red)=P(orange)=P(yellow)=P(blue)=P(green)=15
Do you get this part?

Answer 24

yea

Answer 25

And do you know combinations?

Answer 26

no

Answer 27

I know part of this but I'm not the best at probability so I wouldn't trust my calculations, I know a few people who can though

Answer 28

I hope I made it a bit clearer

Answer 29

yea thanks @LearningIsAwesome

Answer 30

no problem here I'll tag some people

Answer 31

@ganeshie8 @phi you guys know this better than I do

Answer 32

to get one orange, you picked either

Orange + something else
or
something else + Orange

The probability of picking an Orange is 1/5
the probability of picking something else is 4/5

so Pr(O and other)= Pr(O)*Pr(other) = 1/5 * 4/5 = 4/25
the other order other then O also gives 4/25
in total 4/25 + 4/25 = 8/25

Answer 33

thanks @phi

Answer 34

another way to do this is say, Pr( one Orange) = 1 - Pr(2 Oranges) - Pr(no Oranges)
Pr (2 Oranges) is 1/5*1/5= 1/25
Pr (no Orange) is 4/5 * 4/5 = 16/15

and Pr( 1 Orange) = 1 - 1/25 - 16/25 = 1 - 17/25
= 25/25 - 17/25 = 8/25