A bag contain 5 red balls and 4 white balls. Three balls are withdrawn

Question

A bag contain 5 red balls and 4 white balls. Three balls are withdrawn without replacement. What is the probability of drawing at least 2 red balls?

A. 5/42
B. 5/18
C. 17/42
D. 25/42
E. 13/18

CrackverbalGMAT · Accepted Answer

There are a total of 9 Red balls. We need to to draw at least 2 red balls = P(2 red balls) + P(3 red balls)

Since we are drawing without replacement, the favorable outcomes (in this case) and Total outcomes will reduce after each draw. Also Order matters.

P(2 Red balls). Lets assume we are drawing in the RRW order.

P(first red, second red and 3rd white) = 5/9 * 4/8 * 4/7 = 10/63

Different ways of drawing = 3! / 2! = 3 = RRW, RWR, WRR

Therefore total ways of drawing 2 balls = 10/63 * 3 = 10/21

P(3 Red Balls) = 5/9 * 4/8 * 3/7 = 5/42

Therefore the required probability = 10/21 + 5/42 = 25/42

Option D

Arun Kumar

Neodymium · Answer

Favorable outcomes out of drawing 3 balls = 2R1W + 3R
p(drawing 2 red balls atleast) 
=(no. of ways of drawing 2 red (5C2) and 1 white (4C1) + no. of ways of drawing 3 red (5C3) ) / no. of ways of drawing 3 balls (9C3)
= (5C2 x 4C1)/9C3 + (5C3)/9C3 
= 40/84 + 10/84 
= 50/84 
= 25/42

vasu1104 · Answer

red = 5
white= 4
total =9

no replacement allowed
draw 3 balls

find: P (at least 2 red)=

2 case here.

case- 1 2 red, 1 white.

for this, 3!/2! = 3 ways.

since no replacement, RRW
5/9 * 4/8 * 4/7. and there are 3 ways.
so, 3{5/9* 4/8 * 4/7}

now case 2, all 3 red/ for that only one way.
so, 5/9 * 4/8 * 3/7

add both cases.

we get 25/42

option D

vasu1104 · Answer

red = 5
white= 4
total =9

no replacement allowed
draw 3 balls

find: P (at least 2 red)=

2 case here.

case- 1 2 red, 1 white.

for this, 3!/2! = 3 ways.

since no replacement, RRW
5/9 * 4/8 * 4/7. and there are 3 ways.
so, 3{5/9* 4/8 * 4/7}

now case 2, all 3 red/ for that only one way.
so, 5/9 * 4/8 * 3/7

add both cases.

we get 25/42

option D

A bag contain 5 red balls and 4 white balls. Three balls are withdrawn

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A bag contain 5 red balls and 4 white balls. Three balls are withdrawn

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