Multi Stage Events Help Pls. (1 Viewer)

[Earache]

Pretty much ive covered the topic, however my only problem is finding " at most "

For example, The weather bureau has predicted that there is a 25% probability of rain on each of the next 3 days. What is the probability it will rain on,

- all of the next 3 days 25/100 x 25/100 x 25/100 = 1/64
- none of the next 3 days 75/100 x 75/100 x 75/100 = 27/64
- at least one of the next 3 1 - 27/64 = 37/64
- AT MOST 1 of the next 3 days ???????

( Answer = 27/32 )
Thank you.

 

[tacogym27101990]

the probability of it raining 0 days is, as u proved, 27/64
and the probability of it raining only one day is 3 x (3/4 x3/4 x 1/4) as it can rain on either the first, 2nd or 3rd day. this equals27/64

and the probability of it raining NO MORe than one day is the probability of it raining no days PLUS the probability of it raining 1 day

therefore 27/64 + 27/64 = 54/64 = 27/32

 

[PC]

Don't forget the usefulness of the Probability of Complementary Events.

You've already worked out P(rain on 3 days) = 1/64
Now, P(rain on 2 days) = 3 x (3/4 x 1/4 x 1/4) = 9/64
So, P(rain on at most 1 day) = 1 – P(rest)
= 1 – P(rain on 2 or 3 days)
= 1 – (1/64 + 9/64)
= 27/32