M4maths Previous Puzzles

20 Jul 2022 Probability

A bag contains 5 Blue, 6 Green, 3 Yellow and 4 Red balls. If four balls are selected at random, then what is the probability that there exist at least two red balls ?

OPtion

1) 2/9
2) 1/20
3) 301/1530
4) 134/765
5) 67/170
6) 1/204
7) 67/340
8) 57/340
9) 134/340
10) None of these

Solution

Total ways of selecting 4 balls out of 18 = 18C4 = 3060
Out of the 4 balls at least 2 red colour is possible when, there are (2 Red+2 Non-Red) or (3 Red + 1 Non-Red) Or All Four Red
.'. Ways of selecting at least 2 red balls = (4C2 x 14C2) + (4C3 x 14C1) + 4C4 = 546 + 56 + 1 = 603
Hence, required probability = 603/3060 = 67/340
Correct Option 7)

Correct Option: 7 Best Solution (2)

G.S.Kantharao   2 years AGO

Combinations
2 Red+2Non-Red,
3 Red+1 Non-Red
4 Red
Feasible out comes =4c2*14c2+4c3*14c1+4c4+14c0=6*91+4*14+1
=546+56+1=603
Out comes 18c4=18*17*16*15/4*3*2*1=3060
Probability=603/3060
=67/340
My option is 7👈

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RAMADURAI NATESAN   2 years AGO

4 red , 14 non-red (NR)balls. total 18
Favorable events are2R,2NR,/3R,1NR/and 4R
P = (4C2*14C2 + 4C3*14C1 + 4C4 ) / 18C4 = 67/340

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