Probability Part 1

Given that, no of trials =n
Probability of success (p)=‌

1

4

∴ Probability of no success =1−‌

1

4

=‌

3

4

As we know, probability of at least one success =1 - probability of no success
∴ According to the question,
1 - (Probability of no success in n trials )≥‌

9

10

⇒1−P(x=0)≥‌

9

10

⇒1−‌nC0(‌

1

4

)0(‌

3

4

)n≥‌

9

10

⇒1−(‌

3

4

)n≥‌

9

10

⇒(‌

3

4

)n≤‌

1

10

⇒(‌

4

3

)n≥10
[Taking log on both sides]
‌⇒n(log104−log103)≥log1010
‌⇒n(log104−log103)≥1
‌⇒n≥‌

1

(log104−log103)