Question

In the fall, you go to the local nursery and purchase a package of 10 rose plants. The clerk informs you that on average you can expect 5% of the plants to not live through the winter. Assume that the plants are a random sample.

a) Use the binomial formula to determine the probability that one or more of the plants will not survive the winter.
b) What is the probability that all the plants will survive? Write how the binomial formula is used to calculate the probability.

Answer 1

@jim_thompson5910

Answer 2

a)

what is the probability that 0 plants will not survive the winter?

Answer 3

ie what is the probability that all plants survive?

Answer 4

ummm how do i find that

Answer 5

well the chances of one plant not making it (independent of the others) is 5%

so the chances of it surviving is 95%

Answer 6

Ok! so a is 95 percent?

Answer 7

there are 10 plants, so the chances of all 10 plants making it is

(0.95)^10 = 0.59873693923838

which is about a 59.87% chance

Answer 8

Ohhh okay, i get that! that would be the answer for (a)

Answer 9

now how can we use this to answer part a)

Answer 10

you mean part b?

Answer 11

think about it like this

you have 2 possibilities

a) all plants survive

OR

b) at least one (or more) dies

Answer 12

no I haven't givin the answer to anything yet

Answer 13

given*

Answer 14

ok

Answer 15

so if we know that the probability that all plants survive is 0.5987369 roughly

and we have the two choices (given above) then the probability of at least one dying is what?

Answer 16

um..

Answer 17

remember all probabilities must add to 1

Answer 18

41?

Answer 19

think of a coin flip, you can either get heads or tails

both have a chance of 0.5

so 0.5 + 0.5 = 1

Answer 20

41 is way too big

Answer 21

0.5987369 + x = 1?

Answer 22

it need to be a number less than 1

Answer 23

needs*

Answer 24

yes solve that for x

Answer 25

.4012631

Answer 26

good

Answer 27

ok

Answer 28

and I just looked at part b again and I realized that I have answered it unintentionally

Answer 29

part b is asking what is the probability that all plants survive and it's roughly 0.5987369

Answer 30

Okay yah!
what about a?

Answer 31

what you got: 0.4012631

Answer 32

basically

P(all plants survive) + P(at least one dying) = 1

because those are the only two options

Answer 33

oK:) so its : (a)

(0.95)^10 = 0.59873693923

0.5987369 plus x = 1?
x = 0.4012631 <-----


(b)

P(X = 10)

= (0.95)^10

= 0.5987369 <----

Answer 34

it's kinda like saying

P(plant living) + P(plant dying) = 1

since a plant can only live or die

Answer 35

good on both

Answer 36

is the answer i put right

Answer 37

ok thanks!
can u look at my new problem? its just one more and its easier!!

Answer 38

alright