2) Consider a probability space where outcomes are not equally likely. For examp

Question

2) Consider a probability space where outcomes are not equally likely. For example, in the arcade game called Skee Ball, players roll a ball up a ramp and it lands in different areas, which are worth different points ranging from 10 to 50. Since the areas are of different sizes, if a ball is rolled randomly up the ramp, the probabilities that the ball lands in different areas are not equal. Assume that the following probabilities are associated with the different areas: Value 10 points 20 points 30 points 40 points 50 points Probabili 0.5 0.25 0.15 0.08 0.02 If a player rolls 3 balls at random: a) What is the probability of a total score of at least 100 points?

Explanation / Answer

here total score of at least 100 can happen if three balls drawn are ={6 permutation of (10,40,50) +3 permutation of {10,50,50} +6 permutation of {20,30,50)+3 permutations of {20,40,40}+6 permutations of {20,40,50}+3 permutations of {20,50,50}+ 3 permutations of {30,40,40}+6 permutations of {30,40,50}+3 permutations of {30,50,50}+1 permutations of {40,40,40}+3 permutations of {40,40,50}+3 permutations of {40,50,50}+1 permutations of {50,50,50})

=6*0.5*0.08*0.02+3*0.5*0.02*0.02+6*0.25*0.15*0.02+3*0.25*0.08*0.08+6*0.25*0.08*0.02+3*0.25*0.02*0.02+3*0.15*0.08*0.08+6*0.15*0.08*0.02+3*0.15*0.02*0.02+1*0.08*0.08*0.08+3*0.08*0.08*0.02+3*0.08*0.02*0.02+1*0.02*0.02*0.02 =0.0229

please revert for any clarification required/

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