6.2 – Binomial Probabilities You are at your ACT test, you have 3 problems left to do in 5 seconds. You decide to guess on all three, since you don't have.

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Presentation transcript:

6.2 – Binomial Probabilities You are at your ACT test, you have 3 problems left to do in 5 seconds. You decide to guess on all three, since you don't have time to read them. What is the probability that you will get 0, 1, 2, or all 3 questions correct?

Features of a Binomial Experiment: 1.There are a fixed number of trials (n) 2.The n trials are independent and repeated under identical conditions. (Replacing vs Not replacing for example) 3.Each trial has only two outcomes: success (S) and failure (F) 4.For each individual trial, the probability of sucess is the same. (p) The probability of failure (q) would be 1 - p. 5.The central problem of a binomial experiment is to find the probability of r success out of n trials.

Guided Exercise #4 As whole group, turn to page 218 – Look-over answers – Whole group clarification

Example You are at your ACT test... the probability that you will get 0, 1, 2, or all 3 questions correct? (Each question has 4 choices) OutcomesP(Outcome)r

Think about the number of successes that could occur if you had had 10 questions left ~ think about the math involved..... Formula for the binomial probability distribution: (P.220) Where… n = number of trials p = probability of success on each trial q = 1 - p = probability of failure on each trial r = random variable representing the number of successes out of n trials 0 < r < n ! = Factorial..... Cn,r?number of combinations possible of each r value

Example 10 trials, probability of success is 59%. What is the probability of 6 successes? n = 10 p =.59 q = ___ r = 6

Guided Exercise #5 As whole group, turn to page 223 – Cover answers – Whole group clarification IMPORTANT!!!!

More Vocabulary P. 224 in text book Wording is important….

Checkpoint  List defining features of a binomial experiment  Compute binomial probabilities using the formula  Compute binomial probabilities using the table  Use the binomial probability distribution to solve real-world applications.

Homework Read Pages – Take notes on what we have not covered Do Problems – Page (1-17) odds Check odds in back of book Read and preload 6.3 information – Notes/vocab