1. ## Probability

i have been given this question

A whole saler buys items at £35 each. the whole saler sells these in batches of 7 to retailers at £54 per item. It is Known that, on average, 16 items in a thousand are faulty.

(a) Construct the probability distribution table for the number of faulty items in a batch of 7 items. all probability values must be rounded off to 5 decimal places.

2. Originally Posted by ardsuggy
i have been given this question

A whole saler buys items at £35 each. the whole saler sells these in batches of 7 to retailers at £54 per item. It is Known that, on average, 16 items in a thousand are faulty.

(a) Construct the probability distribution table for the number of faulty items in a batch of 7 items. all probability values must be rounded off to 5 decimal places.

This is a Binomial probability distribution. Let $\displaystyle Y$ be the random variable which represents the number of faulty items in a batch of 7 items, we have:

$\displaystyle P(y)=\binom{n}{y}p^y(1-p)^{n-y}$

where $\displaystyle n=7$ and the probability of a given item is faulty is given by $\displaystyle p=\frac{16}{1000}=0.016$. Now you can use the formula to calculate the probability of no faulty item found in a batch (i.e $\displaystyle P(Y=0)=P(0)$); the probability of exactly one faulty item found in a batch (i.e $\displaystyle P(Y=1)=P(1)$) ... etc.

Roy

3. Thank you for your help Roy
it has helped me to understand
thank you