ચાર વ્યક્તિઓ ટાર્ગેટને તાકી શકે તેની સંભાવના અનુક્રમે \(\frac{1}{2},\frac{1}{3},\frac{1}{4}\) અને \(\frac {1}{8}\) છે. જો બધા સ્વતંત્ર રીતે ટાર્ગેટને તકવાનો પ્રયત્ન કરે છે તો ટાર્ગેટ ને તાકી શકાય તેની સંભાવના મેળવો.

A \(\frac{{25}}{{32}}\)
B \(\frac{{25}}{{192}}\)
C \(\frac{{7}}{{32}}\)
D \(\frac{{1}}{{192}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{{25}}{{32}}\)

Step-by-step Solution

Detailed explanation

Let persons be \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) \(P(H i t)=1-P\) (none of them hits) \(=1-\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}} \cap \overline{\mathrm{C}} \cap \overline{\mathrm{D}})\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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