Howard is playing a carnival game. The object of the game is to predict the sum you will get by spinning spinner A and then spinner B. Howard predicts.

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Presentation transcript:

Howard is playing a carnival game. The object of the game is to predict the sum you will get by spinning spinner A and then spinner B. Howard predicts he will get a sum of 5. 1)List the sample space. 2)What is the probability Howard gets a sum of 5? 3)Suppose that Howard gets a 3 on Spinner A, what is the new probability of him getting a sum of 5? 3/12 or 1/4 1/3

CCGPS Geometry UNIT QUESTION: What connection does conditional probability have to independence? Standard: MCC9-12.S.CP.1-7 Today’s Question: How can I find conditional probabilities from a frequency table or the formula? Standard: MCC9-12.S.CP.2-6

Conditional Probability

Conditional Probability contains a condition that may limit the sample space for an event. You can write a conditional probability using the notation - This reads “the probability of event B, given event A”

The table shows the results of a class survey. Find P (own a pet | female) The condition female limits the sample space to 14 possible outcomes. Of the 14 females, 8 own a pet. Therefore, P(own a pet | female) equals Do you own a pet?YesNo Female86 Male57

The table shows the results of a class survey. Find P (wash the dishes | male) The condition male limits the sample space to 15 possible outcomes. Of the 15 males, 7 did the dishes. Therefore, P(wash the dishes | male) 7 15 Did you wash the dishes last night? YesNo Female76 Male78

Using the data in the table, find the probability that a sample of not recycled waste was plastic. P (plastic | non-recycled) The probability that the non-recycled waste was plastic is about 13%. = P(plastic | non-recycled) = MaterialRecycledNot Recycled Paper Metal Glass Plastic Other

Conditional Probability Formula For any two events A and B from a sample space with P(A) does not equal zero

Researchers asked people who exercise regularly whether they jog or walk. Fifty-eight percent of the respondents were male. Twenty percent of all respondents were males who said they jog. Find the probability that a randomly selected jogs given they are male. Relate:P( male ) = 58% P( male and jogs ) = 20% Define:Let m = male. Let j = jogs. The probability that a male respondent jogs is about 34%. Write:P( j | m ) = P( m and j ) P( j ) = Substitute 0.2 for P(A and B) and 0.58 for P(A) Simplify

The table shows the results of a class survey. Find P (own a pet | female) Conditional Probability – Pets Revisited Therefore, P(own a pet | female) equals. 4 7 yesno female86 male57 Do you own a pet? 14 females; 13 males

Classwork The Conditions are Right Task

Homework Practice Worksheet