Question

A bag has 13 red, 14 green and 15 black balls. The probability of getting exactly 2 blacks on pulling out 4 balls is Now the number of each colour ball is doubled and 8 balls are pulled out. The probability of getting exactly 4 blacks is $P _ { 2 }$ Then

• A. $P _ { 1 } = P _ { 2 }$
• B. $P _ { 1 } > P _ { 2 }$
• C. $P _ { 1 } < P _ { 2 }$
• D. None of these

Answer 1

Answer: (B)

$P _ { 1 } > P _ { 2 }$

Answer 2

$P _ { 1 } = \frac { { } ^ { 15 } C _ { 2 } \times { } ^ { 27 } C _ { 2 } } { { } ^ { 42 } C _ { 4 } } = \frac { 27 } { 82 }$

and $P _ { 2 } = \frac { { } ^ { 30 } C _ { 4 } \times { } ^ { 54 } C _ { 4 } } { { } ^ { 84 } C _ { 8 } } = \frac { 17.29 .45 .53 } { 11.79 .82 .83 }$

(After simplification) Hence $P _ { 1 } > P _ { 2 }$