InterviewSolution
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InterviewSolution
| 1. |
P (A ∪ B) = P (A ∩ B) if the relation between P (A) and P (B) is : (a) P (A) + P (B) = 2P (A ∪ B) (b) P (A) + P (B) = 2P (A) P (A ⁄ B) (c) P (A) + P (B) = 2P (A) P (B ⁄ A) (d) none of these |
| Answer» <p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Correct option (c) P (A) + P (B) = 2P (A) P (B ⁄ A) </strong></span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Explanation:</strong></span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">We have P (A ∪ B) = P (A) + P (B) − P (A ∩ B) ...(1) </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">Since P (A ∪ B) = P (A ∩ B) [given] </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">P (A ∩ B) = P (A) + P (B) − P (A ∩ B) [from (1)] </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">⇒ 2P (A ∩ B) = P (A) + P (B) </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">⇒ P (A) + P (B) = 2P (A ∩ B) </span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">⇒ P (A) + P (B) = 2P (A) P (B ⁄ A).</span></span></p> | |