Probability

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kev1804

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In a simple model of the weather in March, each day is classified as either fine or
rainy. The probability that a fine day is followed by a fine day is 0.8. The probability
that a rainy day is followed by a fine day is 0.4. The probability that 1 March is fine
is 0.75 (you may use tree diagram).
(i) Find the probability that
a) 2 March is fine day,
b) 3 March is fine day.
(ii) Find the conditional probability that 3 October is rainy, given that 1 October
is fine day.
(iii) Find the conditional probability that 1 October is fine, given that 3 October is
rainy
pls help me am stuck...
 
a)

the answer is [MATH]\frac{3}{5}[/MATH]
check your book and tell me
 
[MATH]\text {P(certainty)} \equiv 1.[/MATH]
[MATH]\text {P(impossibility)} \equiv 0.[/MATH]
[MATH]\text {P(A or B)} \equiv \text {P(A)} + \text {P(B)} - \text {P(A and B)}.[/MATH]
[MATH]\text {P(A and B)} = 0 \iff \text {A and B are mutually exclusive.}[/MATH]
[MATH]\text {P(C)} \ne 0 \implies \text {P(D given C)} \equiv \dfrac{\text {P(C and D)}}{\text {P(C)}}.[/MATH]
[MATH]\text {P(C)} \ne 0 \text { and } \text {P(D)} = \text {P(D given C)} \iff \text {D is independent of C}.[/MATH]
Those are the basic definitions of probability theory, the small number of tools you have to work with. The trick to using those tools is how to determine what A, B, C, or D are for each particular problem.

Q = March 1 is fair and March 2 is fair
R = March 1 is fair and March 2 is rainy
S = March 1 is rainy and March 2 is fair
T = March 1 is rainy and March 2 is rainy.

Does P(Q or S) have the same meaning as P(March 2 is fair)?

Are Q and S mutually exclusive?

What is the numerical value of P(Q)?

What is the numerical value of P(S)?
 
You can't do part ii and iii because they never told you anything about the weather in October. So the correct answer is these two problems is that they can not be done.

Now that we settled what the answers for ii and iii should be I suggest that you still try to do these two parts. Just assume that the weather in October follows the same rules as the weather in March.
 
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