Can You Solve These Intriguing Probability Puzzles?

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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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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?

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