If `P(A)=3//5 " and " P(B)=2//3`, then which of the following alternatives is incorrect ?A. `P(A cup B) ge 2//3`B. `4//15 le P(A cap B) le 3//5`C. `2//5 le P(A//B) le 9//10`D. `P(A cap overline(B)) ge 1//3`

If `P(A)=3//5 " and " P(B)=2//3`, then which of the following alternat

1.	If `P(A)=3//5 " and " P(B)=2//3`, then which of the following alternatives is incorrect ?A. `P(A cup B) ge 2//3`B. `4//15 le P(A cap B) le 3//5`C. `2//5 le P(A//B) le 9//10`D. `P(A cap overline(B)) ge 1//3`
Answer» Correct Answer - D Since `B sube A cup B`. Therefore, `P(B) le P(A cup B) implies P(A cup B) gt 2//3`. So, alternative (a) is correct. Now, `P(A cap B) =P(A)+P(B)-P(A cup B)` `implies P(A cap B) ge P(A)+P(B)-1` `implies P(A cap B) ge (3)/(5)+(2)/(3)-1=(4)/(15)` Also, `A cap B sube A` `implies P(A cap B) le P(A) implies (A cap B) le 3//5` `therefore (4)/(15) le P(A cap B) le (3)/(5)` So, alternative (b) is correct. Now, `(4)/(15) le P(A cap B) le (3)/(5)` `implies (4)/(15) le P(A//B)P(B) le (3)/(5)` `implies (4)/(15) le (2)/(3) P(A//B) le (3)/(5) implies (2)/(5) le P(A//B) le (9)/(10)` So, alternative (c ) is correct. Finally, `P(A cap overline(B))=P(A)-P(A cap B) le (3)/(5)-(4)/(15)=(1)/(3)` So, alternative (d) is also incorrect.

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If `P(A)=3//5 " and " P(B)=2//3`, then which of the following alternatives is incorrect ?A. `P(A cup B) ge 2//3`B. `4//15 le P(A cap B) le 3//5`C. `2//5 le P(A//B) le 9//10`D. `P(A cap overline(B)) ge 1//3`

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