Siddimaula

Happy to clarify them further. The decoupling of the two probabilities and reshuffling some verbiage may paint the picture more clearly.

Mutually exclusive and exhaustive event
>>And there is a .30 probability that a start-up next year will come up with a better search algorithm than google.<<

Interpretation:
The probability of better search algorithm: P(S) = 0.3
The probability of no better search algorithm: P(Sc) = 0.7

Description:
Both P(S) and P(Sc) are mutually exclusive, exhaustive events, and equal 1.

Conditional Probability
>>google expects to earn $50/share from increased advertising revenue if their total page views exceed 100 trillion times next year. The probability of this happening is .001.<<

Interpretation:
The probability of earnings of $50/share given page views are exceeded: P(A|S) = 0.001

I realize that 'S' in P(A|S) needs to match 'S' in P(S) - essentially, the 'S' represents the mutually exclusive and exhaustive event, which needs to be exactly the same for both P(A|S) and P(S).

Therefore,
The probability of earnings of $50/share given start-up with better search algorithm: P(A|S) = 0.001
The probability of earnings of $50/share given start-up with no better search algorithm: P(A|Sc) = 0.2

Description:
The probability of earnings of $50/share 'given that' the start-up comes up with a better search algorithm, is .001. In contrast, the probability of earnings of $50/share 'given that' the start-up does not come up with a better search algorithm, is 0.2.

Unconditional Probability
>>The total probability that google will meet its earnings target if the page views are exceeded AND a start-up fails to deliver is 0.0007<<

Interpretation:
The unconditional probablility of earnings: P(A)

Description:
The probability of meeting earnings target given the page views are exceeded - estimated at .001, times 0.7, the probability that start-up has no better algorithm next year, equals 0.0007.

The above description now is redudant given the conditional probability above has changed. The following holds instead:

The probability of meeting earnings target given the start-up is successful in a better algorithm - estimated at .001, TIMES 0.3, the probability that start-up has a better algorithm next year,
AND
The probability of meeting earnings target given the start-up is not successful in a better algorithm - estimated at .2, TIMES 0.7, the probability that start-up has no better algorithm next year,
EQUALS
the unconditional probability of 0.1403.

Calculation:
P(A) = P(AS) + P(ASc)
P(A) = P(A|S) * P(S) + P(A|Sc) * P(Sc)
P(A) = (0.001*0.3) + (.2*0.7) = 0.1403

Sorry about the long post. In my original example, I was missing the 'P(A|Sc) * P(Sc) ' - this is what I meant by not being entirely clear.