12-2 Conditional Probability Hubarth Algebra II

Conditional probability contain a condition that may limit the sample space for an event. You can write a conditional probability using the notation P(B|A), read “ 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 yesno female86 male57 Do you own a pet? Ex. 1 Finding Conditional Probability

Using the data in the table, find the probability that a sample of non- recycled waste was plastic. The given condition limits the sample space to non-recycled waste. Material RecycledNon-Recycled Paper Metal Glass Plastic Other The probability that the non-recycled waste was plastic is about 15% A favorable outcome is non-recycled plastic. P(plastic | non-recycled) = = Ex. 2 Real-World Connection

Ex. 3 Real-World Connection 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 male respondent jogs. Relate:P( male ) = 58% P( male and jogs ) = 20% Define:Let A = male. Let B = jogs. The probability that a male respondent jogs is about 34%. Write:P( A | B ) = P( A and B ) P( A ) = Substitute 0.2 for P(A and B) and 0.58 for P(A) Simplify

Ex. 4 Making a Tree Diagram A student made the following observations of the weather in his hometown. Use a tree diagram to find the probability that a day will start out clear, and then it will rain. During the mostly clear days, it rained 4% of the time. On 28% of the days, the sky was mostly clear. During the cloudy days it rained 31% of the time. The path containing clear and rain represent days that start out clear and then will rain. P(clear and rain) = P(rain | clear) P(clear) = = The probability that a day will start out clear and then rain is about 1%.

Practice 1. Use the table to find P(female| do not own a pet) yesno female86 male57 2. Find the probability that a sample of non-recylced waste was paper. 3. Eighty percent of an airline’s flights depart on schedule. Seventy-two percent of its flights depart and arrive on schedule. Find the probability that a flight that departs on time also arrives on time. 4. Find the probability that the day will start off cloudy and then will rain.