Well yes, but …
Every small child knows that one and one make two.
Three and two make five.
When you progress to the magic of multiplication, then one times one is one and two times three is six.
And still means plus.
When I was introduced to probability theory half a century ago it was through set theory & the union U or intersection ∩ of sets, which certainly helped to get it clear in my mind & so also helped me to avoid the so-called “conjunction fallacy”.
The now classic illustration of this starts with an Anchoring Vignette - a woman named Linda is described. She is single, in her early 30s, outspoken & clever, a philosophy graduate, interested in issues such as nuclear non-proliferation. When asked which of the following is more likely:
A Linda is a bank clerk
B Linda is a bank clerk and is active in the feminist movement
most people choose B. Which is the wrong answer because the probability of two things being true for the same person is found by multiplying the two probabilities together, & since a probability is a fraction, a number between 0 & 1, the product must be less than either of the two probabilities on its own – except of course when one probability is zero, in which case the chance of the two things occurring together is also zero.
While it is perhaps not surprising that those not trained in probability theory may make this mistake, it is startling that even those who do understand feel uneasy about the case of Linda. Could the theory be wrong?
TO BE CONTINUED
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