A certain type of rocket has 5 ignitors which act independently of the others. Each ignitor has a 5% chance of failing at any point during the launch. What's the probability that at least one ignitor fails during the next launch?

If a seed is planted, it has a 75% chance of growing into a healthy plant.If 8 seeds are planted, what is the probability that exactly 3 don't grow?

You’re a police officer pulling over every car at a checkpoint. You use a breathalyzer on everyone and pay no mind to other signs of sobriety. On a night like this, the chance that a given driver on this road has a blood alcohol content (BAC) over the limit is 2%. The probability of someone with a BAC over the limit testing positive is 100%. The probability of someone who doesn’t have a BAC over the limit testing positive is 5%. If you pull someone over and they test positive, what’s the probability that their BAC is over the limit? Show your work. You may express your answer as a fraction.

A sample survey interviews an SRS of 267 college women. Suppose that 70% of college women have been on a diet within the past 12 months. What is the probability that 75% or more of the women in the sample have been on a diet? Show your work.