Question

Let X~(B6,0.35), find P(X<4|X>2)

Answer 1

@satellite73

Answer 2

@dan815

Answer 3

@misty1212

Answer 4

anyone help please?? I really need to know it for my exams tomorrow D:

Answer 5

What kind of problem is this

Answer 6

stats @optiquest

Answer 7

i think i might have an idea
but not sure
the question is what it the probability of less that 4 successes given that there are greater than 2 right?

Answer 8

are you using a table of some kind?

Answer 9

@misty1212 yes

Answer 10

there is no table provided but I made my own

Answer 11

are you allowed to use a calculator? if so, which type do you have?

Answer 12

gdc ti-84 plus; yes you can use calc @jim_thompson5910

Answer 13

I don't know what the gdc stands for, but I do have a TI84 plus

you can use the TI84 plus to find binomial probabilities quickly

hit the "2nd" key, then hit the "vars" key

then scroll down to "binomcdf"

the binomcdf function has this basic template

binomcdf(trials, probability, value)

http://tibasicdev.wikidot.com/binomcdf

so you'll type in 6 for the trials, then 0.35 for the probability. The "value" is the value k such that \(\Large P(B \le k) = m\) is true. The value of m is the result of the binomcdf function

Answer 14

Example:

calculating P(X <= 4)

binomcdf(6, 0.35, 4) = 0.977678

Answer 15

@jim_thompson5910 I know how to do that, but for this particular question, P(X<4|X>2), what are the steps you have to take?

Answer 16

first you need to find P(X > 2)

use this idea

\[\Large P(X \le 2) + P(X > 2) = 1\]
\[\Large P(X > 2) = 1 - P(X \le 2)\]

Answer 17

to calculate \(\Large P(X \le 2)\) you would type in binomcdf(6, 0.35, 2)

Answer 18

Yep I did that. for this question, I tried doing P(X>2)/P(X<4) but its not correct...?

Answer 19

Conditional Probability

\[\Large P(A | B) = \frac{P(\text{A and B})}{P(B)}\]

Answer 20

A = event that X < 4
B = event that X > 2

Answer 21

so its P(X>2) x P(X<4) all divided by P(X<4)?

Answer 22

won't it just be P(X>2)

Answer 23

P(A and B) = P(X < 4 and X > 2) = P(X = 3) = ??

Answer 24

you use the binompdf for single binomial probabilities (as opposed to binomcdf which adds up a bunch of probabilities)

Answer 25

@jim_thompson5910 what do you mean?

Answer 26

what is the probability that X = 3?

Answer 27

0.8825.... but why do you need this number?

Answer 28

no you don't type in binomcdf(6, 0.35, 3) for this part

you type in binompdf(6, 0.35, 3)

Answer 29

ohhh oops. so its 0.2354

Answer 30

ahh i get it now!! the answer is 0.667. thank you so much!

Answer 31

A = event that X < 4
B = event that X > 2

\[\Large P(A | B) = \frac{P(\text{A and B})}{P(B)}\]

\[\Large P(X < 4 | X > 2) = \frac{P(X < 4 \text{ and } X > 2)}{P(X > 2)}\]

\[\Large P(X < 4 | X > 2) = \frac{P(X = 3)}{P(X > 2)}\]

\[\Large P(X < 4 | X > 2) = \frac{0.2354909375}{0.35291484}\]

\[\Large P(X < 4 | X > 2) = \frac{0.2354909375}{0.35291484}\]

\[\Large P(X < 4 | X > 2) = 0.66727411491112\]

Answer 32

yes correct

Answer 33

@jim_thompson5910 thank you so so so much!! would you be able to help me in another question?

Answer 34

sure