A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

Question

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is (A) (2/7) (B) (3/7) (C) (5/7) (D) (5/6)

Tardigrade Admin · Accepted Answer

( 5 C 2+ 6 C 2/ 2 C 2+ 3 C 2+ 4 C 2+ 5 C 2+ 8 C 2)=(10+15/1+3+6+10+15) =(25/35)=(5/7)

Q. A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

$\frac{2}{7}$

$\frac{3}{7}$

$\frac{5}{7}$

$\frac{5}{6}$

$\frac{^{5} C _{2} + ^{6} C _{2}}{^{2} C _{2} + ^{3} C _{2} + ^{4} C _{2} + ^{5} C _{2} + ^{8} C _{2}} = \frac{10 + 15}{1 + 3 + 6 + 10 + 15}$
$= \frac{25}{35} = \frac{5}{7}$