UPSC NDA Math Model Paper 6

For every 3 trials, the experiment succeeds 2 times and fails 1 time.
∴ Probability of success: p=

2

3.

For at least 4 success in 6 trials, n = 6 and k = 4, 5, 6. The required probability is therefore:
‌6C4(

2

3

)4(1−

2

3

)6−4+‌6C5(

2

3

)5(1−

2

3

)6−5 +‌6C6(

2

3

)6(1−

2

3

)6−6
=(15)(

2

3

)4(

1

3

)2+(6)(

2

3

)5(

1

3

)1 +(1)(

2

3

)6(

1

3

)0
=

240

729

+

192

729

+

64

729

=

496

729

.