For a certain probability experiment, the probability that event F wil

Question

For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?

I 1/5
II. 1/4
III. 3/5

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

I 1/5
II. 1/4
III. 3/5

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Archit3110 · Answer

P of F ; 1/4 and P of G ; 3/5
both ; 1/4*3/5 ; 3/20 ; 
OPTION D ;

Lipun · Answer

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

IanStewart · Answer

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).

mSKR · Answer

1/4 is understood that G occurs when F occurs

but why does it have also an answer 1/5?

Lipun · Answer

Thank you for the detailed explanation  IanStewart  sir.

Thus, the question basically translates to the minimum and maximum value of P(F AND G).
Minimum value will occur when F and G are mutually exclusive. => P(F AND G) = 0
Maximum value will be P(F) = 1/4 (as explained above by Ian sir).

Any value in the range of 0 to 1/4 (both inclusive) could be a possible value of P(F AND G).
Only 1/5 and 1/4 satisfy the range.

Ans: C

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For a certain probability experiment, the probability that event F wil

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For a certain probability experiment, the probability that event F wil

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