Originally Posted by

**lindah** Hi,

I am having trouble with the following question:

During winter it rains on average 18 out of 30 days. Five winter days are selected at random. Find (4 d.p) the probability that:

(a) the first two days chosen will be fine and the remainder wet

My approach is this is an ordered selection:

I have defined p = it will rain = $\displaystyle \frac{18}{30}$ or 0.6

q = 1 - 0.6 = 0.4

= $\displaystyle 0.4^2 \times 0.6^3$

= 0.03456 .... Looks right to me

The answers I have are yielding 0.0124.

(b) more rainy days than fine days have been chosen

P(3 rainy days) = $\displaystyle _5C_3 \times 0.6^3 \times 0.4^2$

P(4 rainy days) = $\displaystyle _5C_4 \times 0.6^4 \times 0.4$

P(5 rainy days) = $\displaystyle _5C_5 \times 0.6^5$

= 0.3456 + 0.2592 + 0.007776 ..... 0.07776

= 0.612576 ...... 0.68256

The answers are yielding 0.7102

I wonder where I am going wrong

TIA for any assistance!