A gambling book recommends the following “winning strategy” for the game of roulette:
Bet $1 on red. If red appears (which has probability ,then take the $1 profit and quit.
If red does not appear and you lose this bet ( which has probability of occurring), make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit.
Let X denote your winnings when you quit.
(a) Find P{X>0}.
(b) Are you convinced that the strategy is indeed a “winning” strategy?
(c) Find E[X].
When system reliability is increased through redundant or backup components, the redundancy principle is applied.
Assume that your alarm clock has a 0.975 probability of working on any given morning.
With one alarm clock, you have a 0.975 probability of being awakened.
What is the probability of being awakened if you use two alarm clocks?
The probability density function of the net weight in pounds of a packaged chemical herbicide is
a. Determine the probability that a package weighs more than 50 pounds.
b. How much chemical is contained in 90% of all packages?
Express the confidence interval using the indicated format. (Based on the percentages of red, orange, yellow, and blue MMs, the confidence intervals are calculated.)
Express 0.0434<p<0.217 in the form of
Find the following probabilities for the standard normal variable z:
(a)
(b)
(c)