Find probabilities using the binomial distribution

Learning Objectives Define probability as a fraction representing favorable outcomes out of total outcomes. Describe a 'binomial' situation as one with two possible outcomes (e.g., success/failure). Find a least common denominator for two fractions with unlike denominators. Convert fractions into equivalent fractions with a common denominator. Add two fractions with unlike denominators to find a combined probability. Subtract two fractions with unlike denominators to compare probabilities. Solve word problems that involve adding or subtracting fractional probabilities from simple binomial scenarios. If you have a 1/2 chance of picking a red marble and a 1/3 chance of picking a blue one, how can we use fractions to compare your chances? 🔴🔵 Today, we are going o...

TermDefinitionExample ProbabilityThe chance of something happening, written as a fraction. The top number (numerator) is the number of ways it can happen, and the bottom number (denominator) is the total number of possible outcomes.The probability of a coin landing on heads is 1/2, because there is 1 head and 2 total sides (heads and tails). Binomial DistributionA special name for any situation where there are only TWO possible outcomes. Think 'bi' like in 'bicycle' (two wheels). The outcomes could be win/lose, yes/no, or heads/tails.Flipping a coin is a binomial event because the only outcomes are heads or tails. Unlike DenominatorsWhen the bottom numbers of two fractions are different. You can't add or subtract them until you make the denominators the same.The f...

Combined Probability Rule (Addition) P(\text{A or B}) = P(A) + P(B) To find the combined chance of two separate events happening, we add their probabilities together. You MUST find a common denominator before you can add the fractions. Probability Difference Rule (Subtraction) P(\text{Difference}) = P(\text{Larger}) - P(\text{Smaller}) To find out how much more likely one event is than another, we subtract the smaller probability from the larger one. You MUST find a common denominator before you can subtract.