Sometimes, you wish to know the probability that at least one outcome will occur.

Examples of at least scenarios:

  • What is the probability that, if you have three children, at least one will be a boy?
  • What is the probability that, if you answer five multiple-choice questions, you will get at least one correct?
  • What is the probability that, if you flip a coin ten times, you will get at least one tail?

The best way to solve these problems is to determine the probability that what you want does not happen . Recall from Lesson 3A that the chance of an event not happening is referred to as a not probability . This occurs when you are dealing with complements.

P ( A ) + P (not A ) = 1

P ( A ) + P ( A ') = 1

 

What is the probability that, if you have 3 children, at least one will be a boy?

Begin by noting that these are independent events. The gender of one child in no way affects the gender of the other children in the family. If you want at least one boy, then the only outcome you do not want is to have all girls. Therefore, determine the probability of having 3 girls. Because you are considering boys and girls, you have a 1-out-of-2 chance to have a girl.

The probability of having at least 1 boy is or 87.5%.