Question

In a small bag of M&Ms, there are 10 orange candies and 4 blue candies. You select 1 candy, eat it, and then select another.

Find P(you select first an orange candy and then a blue candy). Round your answer to the nearest hundredth.

Answer 1

probability first one is orange is the ratio of orange pens to the total

Answer 2

1/10?

Answer 3

*candy

Answer 4

slowly
10 orange candies and 4 blue candies
how many candies are orange?

Answer 5

10

Answer 6

right
and how many are there total, orange and blue

Answer 7

14

Answer 8

14-1 (because you ate one)=13

Answer 9

ok good
so the probability you get an orange one on the first try is
\[\frac{\text{number of orange}}{\text{total number of candies}}=\frac{10}{14}=\frac{5}{7}\]

Answer 10

now that you have eaten an orange candy, how many candies are left in the bag?

Answer 11

13 or 5/6

Answer 12

oh i see, you already answered that as well, there are now 13 in the bag

Answer 13

of those 13, how many are blue?

Answer 14

Uhh 4

Answer 15

right. so now the probability you pick a blue one is
\[\frac{4}{13}\]
take the two numbers,
\[\frac{10}{14}\] and
\[\frac{4}{13}\] and multiply them together to get your answer

Answer 16

that is, compute
\[\frac{5}{7}\times \frac{4}{13}\]

Answer 17

Sorry my stupid computer died. So that would be 20/91

Answer 18

wow you still here?

Answer 19

yes it would be \(\frac{20}{91}\)

Answer 20

this might have seemed like a lot of work, but really it was two short steps
probability first one is orange is \(\frac{10}{14}\) probability that second is blue if you know the first one was orange is \(\frac{4}{13}\) and
\[\frac{10}{14}\times \frac{4}{13}=\frac{20}{91}\]

Answer 21

And if we rounded it to the nearest hundreth it would be 0.22!

Answer 22

Alright what about this one.

Answer 23

In a large bag of Skittles®, each of the 5 colors (red, orange, yellow, blue, green) occurs with the same probability. You reach in and select 2 candies.

Answer 24

Find the probability that exactly one of the candies is orange.

Answer 25

exactly one orange means one orange and one not orange right?

Answer 26

yeah

Answer 27

1/5?

Answer 28

since there are 5 colors, and each has the same probability, the probability of each is \(\frac{1}{5}\) but that is not the answer to your question

Answer 29

Hmm. So that means that they all have 1/5 chance of being selected but that isn't saying that one of them will be orange

Answer 30

right

lets say you pick two in succession, first pick and second pick
you want the probability that exactly one of the picks is orange

there are two ways to do this : { orange, not orange} or {not orange, orange}

Answer 31

the probability of both of these is the same
\[\frac{1}{5}\times \frac{4}{5}\] for each

Answer 32

So i get 4/25?

Answer 33

close
\[\frac{4}{25}\] is the probability of each one of these events, but there are two of them, so you have to double it

Answer 34

Double it.. so 16/50?

Answer 35

i am not sure that any of this is making sense to you, but here is what is going on
{ orange AND not orange}
for and you multiply and so it is
\[\frac{1}{5}\times \frac{4}{5}\]
then {not orange AND orange } again is
\[\frac{4}{5}\times \frac{1}{4}\]
since you want either one of these you ADD them and get
\[\frac{4}{25}+\frac{4}{25}=\frac{8}{25}\]

Answer 36

btw
\[2\times \frac{4}{25}=\frac{8}{25}\] don't multiply top and bottom

Answer 37

Ohhhh! See I was totally lost. Lol. So 8/25 ?

Answer 38

yes i thought so
it is \(\frac{8}{25}\) yes

Answer 39

So if we divided it, it would be 0.32?

Answer 40

yes

Answer 41

thanks!!

Answer 42

yw