Couple Binomial Probability Questions (1 Viewer)

[GaDaMIt]

During winter it rains on average 18 / 30 days. Five winter days are selected at random. Find correct to four decimal places, the probability that
a) the first two days chosen will be fine and the remainder wet 0.0124
b) more rainy days than fine days have been chosen 0.7102

AND

One bag contains three red and five white balls, and another bag contains four red and four white balls. One bag is chosen at random, a ball is selected from that bag, its colour is noted and then it is replaced
a) find the probability that the ball chosen is red 7/16
b) if the operation is carried out eight times, find the probability that
i) exactly three red balls are drawn ⁸C₃ (9/16)⁵(7/16)³
i) at least three red balls are drawn 1 - (9/16)⁸ - 8(9/16)⁷ (7/16) - ⁸C₂ (9/16)⁶ (7/16) ²


Please talk me through your logic when solving
Thanks for any help

 

[Riviet]

I'll try the first one:

p(wet)=18/30
p(dry)=12/30

a) p(2 wet then 2 fine) = (18/30)².(12/30)²

b) p(3 or more rainy days) = p(3 wet) + p(4 wet) + p(5 wet)
=(18/30)³.(12/30)².5C3 + (18/30)⁴.(12/30).4C1 + (18/30)⁵

 

[GaDaMIt]

I'll try the first one:

p(wet)=18/30
p(dry)=12/30

a) p(2 wet then 2 fine) = (18/30)².(12/30)²

Well aside from the fact you didnt include a fifth (rainy) day, thats what i did. Answer turns out to be 0.03456, obviously conflicting with the answers cambridge provided