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target,the probability that it hits the centre of the targetis 03.  \nGeorge fires two arrows at the target.  \n(a)Complete the following probability tree diagram.  \nFirst arrow  \nSecond arrow  \ncentre  \n[2]  \n(b)Calculate the probability that George only hits the centre of the target once.  \n1.  \nMAHSDIY  \nAt breakfast,the probability that Melanie has a bowl of cereal is 0·3 and the probability thatMelanie has a slice of toast is 0·2.Melanie having a bowl of cereal and Melanie having a slice of toast are independent events.  \n(a)Complete the tree diagram.  \n[3]  \nMelanie has a  \nslice of toast  \n(b)Find the probability that Melanie has a bowl of cereal and a slice of toast.       [2]  \nMAUHSDIY  \nIn a group of 15 people there are 5 men and 10 women.  \nOne of the men and three of the women are wearing red jumpers.  \nA man is selected at random from the group.  \nThen a woman is selected at random from the group.  \nIs the probability that the people selected are both wearing red jumpers greater or less than 5%?  \nYou must show your working and give a reason for your answer.  \n[5]  \n……………………-……………  \n……………………………………………………………***..…….  \n………………………  \n……………………………………………………………………  \n…………………………………………………………………………………  \n……………………………………………………………………………  \n………………………………………………………………………………………  \n………………………………………  \n…………………………………………………………………………  \n…………………………………………………………………………………………………………  \n……………………………………………………………………………………………………………………………………·  \n……………………………………………………………………………………………  \n……--………………………………………………  \nCarys has a Monday to Friday job and a weekend job.Working Monday to Friday and working weekends are independent events.  \nMAUHSDIY  \nIn any given week,the probability that Carys works every day from Monday to Friday is 0·65.The probability that she works both days during a weekend is 0·2.  \n(a)Complete the following tree diagram.  \n[2]  \nWorks  \nWorks  \nevery day  \nboth days  \nfrom  \nduring a  \nMonday to  \nweekend  \nFriday  \n[2]  \nSunday.  \nMAHSDIY  \nRowena sometimes wears a hat and sometimes wears gloves.  \nThe probability that she wears a hat on a given day is 0·6.The probability that she does not wear gloves on a given day is 02.Wearing a hat and wearing gloves are independent.  \n(a)Complete the following tree diagram.  \n(b)  Calculate the probability that,on a given day,Rowena wears a hat but does not weargloves.[2]  \n(c)Calculate the probability that,on a given day,Rowena does not wear a hat or gloves.[2]………      …   …      ……………      …………  …………    ……         ……………      ………          ……  \n6  \nMAUHSDIY  \nThe probability that Daisy wears a bracelet is 0·7.  \nThe probability that Daisy wears a bracelet and wears a necklace is 0·63.For Daisy,wearing a bracelet and wearing a necklace are independent events.  \nProbability that Daisy wears a necklace =……………………………  \n(ii)Complete the tree diagram.[2]  \nDaisy wearsDaisy wearsa bracelet\u003Ca necklaceDaisy does notwear a necklaceDaisy wearsDaisy doesnot wear abracelet\u003Ca necklace  \n0.7  \nDaisy does notwear a necklace  \n(b)Find the probability that Daisy does not wear a bracelet and does not wear a necklace.[2]……  …………    …………                 ………    ………………   ……………    …………   ……          …………  …    …   ……………     ……………………………            ………   ……………      ……………………………………   …………………………  \nMAUHSDY  \nAlwyn often drives from Bangor to Cardiff.  \nHe always chooses one of two routes for these journeys.He either travels through Rhayader or through Hereford.The probability that he travels through Rhayader is 0·7.  \nSometimes he decides to stop for a break during his jouney.His decision is independent of the route he takes.  \nThe probability that he travels through Rhayader and stops for a break is 0·42.  \n[4]  \n(a)Complete the following tree diagram.  \nStops for  \nRoute  \na break  \n(b)Calculate the probability that Alwyn travels through Hereford but does not stop for abreak.[2]………     ……………    ………………      ……………   ………………     ……………","cbCaik15NQb081aX","https://ap.wps.com/l/cbCaik15NQb081aX","pdf",1314651,"English","# GCSE Topic Booklet\n## Probability tree diagram questions\n## Independent events and joint/complement probabilities\n## Card selection without replacement","[{\"question\":\"How do you complete a probability tree diagram for independent events?\",\"answer\":\"Assign the given probabilities to each branch at every stage, then multiply along paths to get the joint probability for each route.\"},{\"question\":\"What method finds the probability of only one success in two arrows (e.g., hitting the centre once)?\",\"answer\":\"Sum the probabilities of the two mutually exclusive outcomes: first hit then miss, or miss then hit, using the appropriate tree branches.\"},{\"question\":\"How do you calculate probabilities like “neither event A nor event B occurs”?\",\"answer\":\"Use complements: neither happens is the intersection of not A and not B, obtained from the tree diagram and the probabilities of independent events.\"}]","GCSE Topic Booklet - Probability Tree Diagram - Page Exercises | PDF",1792977580,23]