Conditions. Conditional Probability and Tree Diagrams Example Let us consider the following experiment: A card is drawn at random from a standard deck of cards. The coach takes out a ball out from the bag a random then, without replacement, takes out another one. 13 Questions Show answers. Recall that there are 13 hearts, 13 diamonds, 13 spades and 13 clubs in a standard deck of cards. Question 5: William enters a badminton competition. Step 1: Construct the probability tree showing two selections. We use the AND rule via the probability tree, so, \text{P(blue and blue)}=\dfrac{5}{9}\times\dfrac{4}{8}= \textcolor{blue}{\dfrac{20}{72}} \text{ and } \text{P(red and red)}=\dfrac{4}{9}\times\dfrac{3}{8}= \textcolor{red}{\dfrac{12}{72}}, Step 3: Add the probabilities together, by the OR rule for mutually exclusiveevents, to get, \text{P(Same colour)}= \dfrac{20}{72} +\dfrac{12}{72}=\dfrac{32}{72}, Question 1: Anna and Rob take their driving tests on the same day. Previous Independent Events Practice Questions. The probability of both Anna and Rob passing is 0.35. (2)! GCSE IGCSE Maths Mathematics - tree diagrams - independent - conditional - algebraic problems - differentiated practice worksheets with space for answers - solutions included. The probability he wins a game is 0.6. Work out the probability that the two counters Sean removes are the same colour. This means to find the probability of A and B occurring you must multiply the probability of A occurring by the probability of B occurring. We need to understand independent and dependent events to be able to do the next sections. Square Conditional probability trees are similar to probability trees, but the probabilities change depending on the previous events. Adding together the … This website and its content is subject to our Terms and Benjamin plays football for his local team. This is the result of not replacing the first ball hence only leaving 13 balls in the bag to pick from. 4. Rearranging the equation to make P(R_p) the subject: (b)  The probability of both Anna and Rob failing their driving test can be found using a tree diagram as shown below: Hence the probability of them both failing is \dfrac{3}{20} = 0.15. The probability of Anna passing her driving test is 0.7. Draw a tree diagram in your math workbook. (b) Work out the probability that William wins at least one match. \text{P(blue and blue)}=\dfrac{5}{9}\times\dfrac{5}{9}= \textcolor{blue}{\dfrac{25}{81}} \,\, \,\, \text{P(red and red)}=\dfrac{4}{9}\times\dfrac{4}{9}= \textcolor{red}{\dfrac{16}{81}}. There are 9 balls to begin with, reducing to 8 after the first selection, as shown below. The conditional probability of A given B, is the “probability that event A happens given that event B happens”. Picking a red marble at random from a bag, then picking a green marble without replacing the red marble are dependent events. Next Listing Outcomes Practice Questions. probability, trees. Is the coach more likely to pick out two balls that are the same colour or two that are different colours? (b) Work out the probability of both Anna and Rob failing their driving tests. We have a range of learning resources to compliment our website content perfectly. Read each question carefully before you begin answering it. A-Level Edexcel Statistics S1 June 2008 Q1d (Probability Tree diagrams) : ExamSolutions - youtube Video MichaelExamSolutionsKid 2020-02-25T15:02:58+00:00 About ExamSolutions 5(a) In the space below, draw a probability tree diagram to represent this information [3 marks] 5(b) Calculate the probability that one red and one green ball are taken from the bag. Tree Diagrams practice questions + solutions. Example: A bag contains 4 red balls and 5 blue balls. (a) Work out the probability of Rob passing his driving test. Here we have to work out the probability that the coach takes out two balls that are a different colour. If two events, A and B, are independent, then, \textcolor{black}{\text{P}(A \text{ given } B) = \text{P}(A)} \,\, and \,\, \textcolor{black}{\text{P}(B \text{ given } A) = \text{P}(B)}, If two events, A and B are dependent, then, \textcolor{black}{\text{P}(A \text{ and } B) = \text{P}(A) \times \text{P}(B \text{ given } A)}. We know there are a total of 9 balls in the bag so there is a \dfrac{4}{9} chance of picking a red ball. Created: Apr 25, 2013 | Updated: Apr 14, 2015. Calculate the probability that he selects the same coloured ball each time, given that each time a ball is selected, it is not replaced. Adding together the probabilities of the result being blue then blue or green then green: \dfrac{7}{22}+\dfrac{5}{33}=\dfrac{31}{66}, Question 3: The probability that a bus is on time is 0.75. What is the probability that Benjamin starts the game but doesn’t score a goal? For conditional probability questions, when drawing the tree diagram we have to be careful as the probability changes between the two events. registered in England (Company No 02017289) with its registered office at 26 Red Lion Each branch in a tree diagram represents an outcome. A-Level Edexcel Statistics S1 June 2008 Q1d (Probability Tree diagrams) : ExamSolutions - youtube Video MichaelExamSolutionsKid 2020-02-25T15:02:58+00:00 About ExamSolutions We can see that there are two ways of doing this, either blue and blue, or red and red. This topic will look at how tree diagrams can be used to determine the probability of different types of events happening. Make sure you are happy with the following topics before continuing.

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