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A level probability help!!

hi, im kinda stuck on this please could anyone help and show the steps on how to solve this correctly:

When Betty is on holiday she intends to go for a five-mile run before breakfast every day. however sometimes she stays in bed instead. the probability that she will go for a run on the first morning is 0.8. thereafter, the probability that she will go for a run is 0.7 if she went for a run on the previous morning and 0.6 if she did not.

Find the probability that on the first three days of her holiday she will go for:

a) three runs
b) exactly two runs

thanks !!!!

username1560589

For the first one you use the basic probability laws.

P(A \cap B) = P(A)P(B)

, where A and B are independent.

P(R\cup R\cup R) = P(R)P(R)P(R) = P(R)^3

For the second one, you also use this law, but you need to sum the different possibilities.

(edited 9 years ago)

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