Can You Solve These Intriguing Probability Puzzles?

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SUMMARY

This discussion focuses on solving probability puzzles involving various scenarios. The first puzzle calculates the probability of finding two adjacent unoccupied parking spaces among 10 total spaces with 7 already occupied. The second puzzle involves determining the probability that person Y hits a target before person X, given their respective hitting probabilities of 2/5 and 1/4. The third puzzle examines the arrangements of the word "MISSISSIPPI," specifically how many arrangements exist with the condition that the two P's must be separated. Lastly, the fourth puzzle calculates the probability of selecting a ball from box P, given the selection process and the distribution of balls in both boxes.

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rayukpant
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1. There are 10 adjacent parking places in the parking lot. When you arrive in your new Chevrolet , there are already 7 cars in the lot. What is the probability that you can find two adjacent unoccupied spaces for your Chevrolet?
2. Two persons X and Y take turns as follows for shooting at a target :X,Y,X,Y,X,……….etc. The probability that X hits the target every time he takes a shot is 2/5 and the probability that Y hits is ¼. The probability that Y hits the target before X is p/q. Determine the values of p and q.
3. In how many ways the word MISSISSIPPI be arranged ? In how many ways can they be arranged if the two P's must be separated?(only the solution for second part is needed )
4. Box P has 2 red balls and 3 blue balls while box Q has 3 red balls and 1 blue ball. A ball is selected as follows :(i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of the boxes P and Q being selected in the process is red, what is the probability that it came from box P?
 
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You need to show some level of effort. What have you tried for each problem?
 
rayukpant said:
1. There are 10 adjacent parking places in the parking lot. When you arrive in your new Chevrolet , there are already 7 cars in the lot. What is the probability that you can find two adjacent unoccupied spaces for your Chevrolet?
2. Two persons X and Y take turns as follows for shooting at a target :X,Y,X,Y,X,……….etc. The probability that X hits the target every time he takes a shot is 2/5 and the probability that Y hits is ¼. The probability that Y hits the target before X is p/q. Determine the values of p and q.
3. In how many ways the word MISSISSIPPI be arranged ? In how many ways can they be arranged if the two P's must be separated?(only the solution for second part is needed )
4. Box P has 2 red balls and 3 blue balls while box Q has 3 red balls and 1 blue ball. A ball is selected as follows :(i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of the boxes P and Q being selected in the process is red, what is the probability that it came from box P?

Have you read the rules for this forum? We don't do homework, and you are required to show some effort.

RGV
 

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