Question

Is the following situation a binomial setting? explain how it does or does not meet the conditions of a binomial setting. Draw a single card from a standard deck of cards. Observe the card and then place it. Count the number of times you draw a card like this until you get a seven

Answer 1

what is the probability of drawing a seven each time?

Answer 2

1/52

Answer 3

actually there are four 7's in a standard deck, so 4/52
what is the probability of not getting seven?

Answer 4

right

Answer 5

0.077

Answer 6

what is the probability of not getting seven?

Answer 7

is it 1/52 or 1/48

Answer 8

it is neither. the probability of something happening plus the probability of it not happening must always be equal to 1.

Answer 9

only two choices, success= seven failure= any other card
each draw is independent because the card is replace each time. Draw until you observe a 7 the probability of success, p=4/52=1/3

Answer 10

right, so does that fit the definition of a binomial probability?

Answer 11

it is geometric

Answer 12

BINOMIAL DISTRIBUTION, POPULATION PROPORTION
n = NUMBER OF TRIALS [ 7 ]
(sample size)
k = NUMBER OF SUCCESSES [ 1 ]
(from 0 up to and including k NUMBER OF SUCCESSES)
p = POPULATION PROPORTION [ 0.08 %]

Answer 13

yes it is geometric but that wasn't part of the question so I ignored it.
where do you get 20 trials from?

Answer 14

where do you get 7 trials from?

Answer 15

does or does not meet the conditions of a bionomial. until you get a seven

Answer 16

Bionomial settingis failure or success

Answer 17

what is the definition of a binomial probability distribution?

Answer 18

right, and do we have that on each trial or not?

Answer 19

no

Answer 20

on each trial, do we not have a chance of success p=4/52 and failure=1-p ?

Answer 21

yes

Answer 22

is that binomial?

Answer 23

so it can be bionomial because it met one of the four conditions

Answer 24

Again, you have to be careful about the definition of a binomial distribution. Binomial distributions have 2 parameters; the probability and the number of trials. Although each trial here is binomial, because we are drawing cards *until* the first 7 is found, the number of trials is not specified. Hence geometric probabilities are never the same as binomial ones.

Answer 25

ok thanks