Probability and Probability Distributions (SCHOOL OF ENGINEERING): example pleas
ID: 3357232 • Letter: P
Question
Probability and Probability Distributions (SCHOOL OF ENGINEERING): example
please show all the work possible for each one!
Probability of winning a price from a randomly bought ‘Florida lottery’ ticket is 0.02. (This does not mean the grand price, it could be any price.) Gambler buys tickets and checks consecutively until he wins a price.
What is the best probability distribution matches with this description?
What is the probability of winning a price exactly in the fourth ticket he buys (attempt)?
What is the probability of winning a price within first four attempts?
What is the probability of having at least four attempts to have a winning ticket?
What is the probability of having at least twenty attempts to have a winning ticket?
What is the expected number of attempts needed to find a winning ticket?
Explanation / Answer
There are two outcomes, whether the gambler wins a price or not, the best distribution is the binomial distribution.
Probability of winning a price = 0.02
=> Probability of not winning a price = 1 - 0.02 = 0.98
Probability of winning a price exactly in the fourth ticket = 0.983 * 0.02 = 0.0188.
Probability of winning a price within first four attempts = 0.02 + 0.98 * 0.02 + 0.98 * 0.98 * 0.02 + 0.0188 = 0.0776.
Probability of having atleast four attempts to have a winning ticket = 0.983 = 0.9412.
Probability of having atleast twenty attempts to have a winning ticket = 0.9819 = 0.8007.
Expected number of attempts needed to find a winning ticket = 1 / 0.02 = 50.
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