Question

Please help me solve this question
Out of 10 loaves on a shelf, 4 are three days old. If the store manager selects 5 loaves at random, what is the probability that:
a) one of the loaves is three days old?
b) x of the loaves is three days old?
In continuation of problem 4 above:
a) Evaluate the probability distribution in problem 4, that is P(x│10,4,5) , for all meaningful values of x,
and summarize the results in a probability distribution table.
b) Plot these values on a coordinate system and show the probability distribution diagram.
c) For what value of x is the probability maximum? What does this imply?

Answer 1

Not a good question. "three days old" could mean EXACTLY or AT LEAST.

Answer 2

How about this question can you help me with this question?

In continuation of problem 4 above:
a) Evaluate the probability distribution in problem 4, that is P(x│10,4,5) , for all meaningful values of x,
and summarize the results in a probability distribution table.
b) Plot these values on a coordinate system and show the probability distribution diagram.
c) For what value of x is the probability maximum? What does this imply?

Answer 3

it is related to the previous question

Answer 4

Assume it means "exactly three days old."
You have sampling without replacement, which is a bit complicated.
For none of them to be 3 days old (you missed sampling one four times):

the probability is (6/10)(5/9)(4/8)(3/7)=0.071

for at least 1 to be 3 days old, P = 1-0.071 = 0.929

For exactly 1 to be three days old, I am kind of stumped, because the probability of hitting it keeps changing as you sample, being (4/10) the first time, then (4/9) the second, (4/8) the third, (4/7) the fourth.
Once you have hit it, however, then the other probabilities are like my first line. That's the best I can do now.

Answer 5

Thank you so much

Answer 6

You are welcome. Sorry not to have been more help.

Answer 7

It's ok it was a great help

Answer 8

The probability that one of the loaves is three days old is given by:
\[P(1\ loaf)=\frac{4C1\times6C4}{10C5}=\frac{4\times6\times5}{2} \times \frac{5\times4\times3\times2}{10\times9\times8\times7\times6}=you\ can\ calculate\]

Answer 9

and how do we solve the next part

Answer 10

\[P(x\ of\ the\ loaves)=\frac{\left(\begin{matrix}4 \\ x\end{matrix}\right)\left(\begin{matrix}6 \\ 5-x\end{matrix}\right)}{\left(\begin{matrix}10 \\ 5\end{matrix}\right)}\]

Answer 11

@kropot72 Wow!