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**Sample space diagrams and tree diagrams**

S1 Probability Sample space diagrams and tree diagrams

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** Sample Space Diagrams + 1 2 3 4 5 6**

Two fair spinners are numbered 1,1,1,2,3 and 1,2,2,3,3. The sum of the two numbers is calculated. Find the probability that the sum is exactly 6 Find the probability that the sum is less than 6 + 1 2 3 4 5 6 P(6) = 2 25 P(<6) = 23 25

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Tree Diagrams Adam and Beth are playing darts. The probability that Adam hits the board with his first dart is 0.4 and the probability that Beth hits the board with her first dart is 0.6. Find the probability that: Both Adam and Beth hit with their first dart At least one of them hits with their first dart B hit P(hit,hit) = 0.4x0.6 = 0.24 0.6 A hit 0.4 0.4 B miss P(hit,miss)=0.4x0.4= 0.16 P(miss,hit)=0.6x0.6= 0.36 0.6 B hit 0.6 P(at least one hit) = = 0.76 A miss B miss 0.4

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Questions Throwing a die and tossing a coin. Find the probability of a head and a 6 Throwing two six sided dice and recording the product of the values. Find the probability that the answer is greater than or equal to 24 Picking one card from each of two different standard packs of cards. What is the probability that the first card is a heart and the second is not a heart? Picking a bead from a pot containing 2 black, 3 white and 1 red beads. Not replacing it and picking a second bead. What is the probability that at least one of the beads is white?

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