Lipun wrote:
Hi
IanStewart sir &
Bunuel sir,
The question doesn't state the relationship between the events F and G. It could very well be that F occurs every time G occurs. The probability of F and G occurring together would then be equal to the probability of event G.
Kindly specify the error in my reasoning.
Thanks
Lipun
It can't be true that F happens every time G happens, because G happens 60% of the time. If F happened every time G did, then F would also happen (at least) 60% of the time. But we know F only happens 25% of the time.
It is possible, though, that G happens every time F happens (and G also happens sometimes when F does not). In the real world, F and G might be events like (in some location) :
G = the probability there are clouds on any given day
F = the probability it rains on any given day
Every time F happens, G also happens, but not the reverse.
If you have two dependent events F and G, and F is less likely than G to happen, then the maximum possible probability both F and G happen will equal the probability F alone happens (because G could happen every time F does).
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