# Simple GCSE Binomial Distribution Question

• Jun 23rd 2010, 03:42 AM
dan9408
Simple GCSE Binomial Distribution Question
Hello posters, i am just wondering if you could help me out here; I have my GCSE exam in two days and having left school without a mark scheme - please could you just tell me the answer to question below so I can see whether i got it right. Thanks in advance.

The probability that a bag of rice weighs less than 260g is 0.3.

Four Bags are chosen at random

What is the probability that exactly one bad weighs less than 260g?
You may use p⁴ + 4pq³ + 6p²q² + 4pq³ + q⁴
• Jun 23rd 2010, 04:11 AM
mr fantastic
Quote:

Originally Posted by dan9408
Hello posters, i am just wondering if you could help me out here; I have my GCSE exam in two days and having left school without a mark scheme - please could you just tell me the answer to question below so I can see whether i got it right. Thanks in advance.

The probability that a bag of rice weighs less than 260g is 0.3.

Four Bags are chosen at random

What is the probability that exactly one bad weighs less than 260g?
You may use p⁴ + 4pq³ + 6p²q² + 4pq³ + q⁴

X ~ Binomial(n = 4, p = 0.3)

$\displaystyle Pr(X = 1) = {4 \choose 1} (0.3)^1 (0.7)^3 = ....$
• Jun 23rd 2010, 04:16 AM
Sudharaka
Quote:

Originally Posted by dan9408
Hello posters, i am just wondering if you could help me out here; I have my GCSE exam in two days and having left school without a mark scheme - please could you just tell me the answer to question below so I can see whether i got it right. Thanks in advance.

The probability that a bag of rice weighs less than 260g is 0.3.

Four Bags are chosen at random

What is the probability that exactly one bad weighs less than 260g?
You may use p⁴ + 4pq³ + 6p²q² + 4pq³ + q⁴

Dear dan9408,

For the Binomial distribution, $\displaystyle b(x;n,\theta)=~^{n}C_{x}\theta^{x}(1-\theta)^{n-x}$
where $\displaystyle x:~Number~of~successes$
$\displaystyle n:~number~of~trials$
$\displaystyle \theta:~probability~of~a~success$

In this case define the success as "a bag of rice weights less than 260g"

Hope you will be able to continue.