Question

A customer from Cavallaro's Fruit Stand picks a sample of 5 oranges at random from a crate containing 65 oranges, of which 6 are rotten. What is the probability that the sample contains 1 or more rotten oranges? (Round your answer to three decimal places.)

Answer 1

"one or more" makes it easy
compute the probability that you get zero rotten ones
subtract that number from 1

Answer 2

you know how to do that?

Answer 3

if not let me know and i can walk you through it
just asking

Answer 4

please walk me through it

Answer 5

we are going to compute the probability that NONE are rotten
first one is not probability is \(\frac{59}{65}\) since there are 59 not rotten ones and 65 all together

Answer 6

second one is not rotten given the first one is not
that is \(\frac{58}{64}\) because we know the first one selected was not rotten leaving 58 ok ones and 64 total because we picked one already

Answer 7

and so one for all 5 not being rotten
in other words
\[\frac{59}{65}\times\frac{58}{64}\times \frac{57}{63}\times \frac{56}{62}\times \frac{55}{61}\]

Answer 8

that is the probability that none of the five chosen are rotten

the probability that one or more is is \(1-\frac{59}{65}\times\frac{58}{64}\times \frac{57}{63}\times \frac{56}{62}\times \frac{55}{61}\)

Answer 9

okay

Answer 10

that is all

Answer 11

thanks

Answer 12

yw