Binomial Probability Issue :( (1 Viewer)

[tashbash332]

During winter it rains on average 18 out of 30 days. Five winter days are selected at random. Find, correct to four decimal places, the probabiity that:
a) the first two days chosen will be fine and the remainder wet,
b) more rainy days than fine days have been chosen

 

[kooliskool]

Hi,

You should note that not every probability is binomial, and you need to learn how to recognise it.

Characteristics of Binomial probability are:

1. There are n independent trials (in here, 5 winter days means 5 trials)
2. Constant probability for every trial (in here, it is, because without replacement)
3. Only two outcomes, success or failure (it rains with a chance of 18/30)
4. Only want the number of success, but not the order of them.

a) So as you can see, it fits into everything except 4 in this part, you have an order, that makes it just normal probability.

Let R be rain and N be not rain,

The probability will be:



b) For this part, all the characteristics are satisfied, since it only wants more rainy days then fine days, which means only care about number of success, not how they are ordered.

Hence:



Which I can't be bothered to get my calculator to get the final answer.

Hope this helps