Probability Part 1

Here is 5 trials.

So according to Bernoulli trial n=5
P( at least one failure )=1−P( no failure )
According to question,
1−P( no failure )≥‌

31

32

⇒1−P(x=5)≥‌

31

32

[Note: no failure = all success]
‌⇒1−‌5C5p5≥‌

31

32

‌⇒1−p5≥‌

31

32

‌⇒p5≤‌

1

32

‌⇒p≤‌

1

2

‌∴p∈[0,‌

1

2

]
Note: p can not be less than 0 as probability is always ≥0 and ≤1.