#### Didn’t find what you are looking for? Probability and combinatorics ### A gambling book recommends the following "winning strategy" for the game of roulette. It recommends that a gambler bet $1 onred. If red appears (which has probablity 18/38), then the gamblershould take her$1 profit and quit. If the gambler loses this bet (which has probablity 20/38 of occurring), she should make additional \$1 bets on red on each of the next two spins of the roulette wheel and then quite. Let X denote the gambler's winnings when she quites. (a) Find P{X > 0}. (b) Are you concinved that the strategy is indeed a "winning" strategy? Explain your answer. (c) Find E[X].

Probability and combinatorics ### A sports team has 7 players. In how many ways can the team select a captain and junior captain?

Probability and combinatorics ### An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is 0.2. What is the probability that the third hole drilled is the first to yield a productive well?

Probability and combinatorics ### A large urn in your kitchen is full of fruit. There are six apples, four oranges, and five pears. What percentage of the mixed fruit are apples? What percentage are not apples?

Probability and combinatorics ### How would adding 50 points to each score affect the mean?

Probability and combinatorics ### If 95% of the population has an IQ between 70 and 130, what is the probability of meeting a person with an IQ either higher than 130 or lower than 70?

Probability and combinatorics ### Prove that $$\displaystyle\sum_{i=1}^{n} \left(\begin{array}{c}i\\ 2\end{array}\right)=\left(\begin{array}{c}n+1\\ 3\end{array}\right)$$ $$\forall n\geq2$$

Probability and combinatorics ### Taylor has a set of 32 cards. There are 16 yellow cards and 16 brown cards in the set. The first 6 cards that Taylor draws are yellow, brown, yellow, yellow, yellow, and brown. Based on these results, what is the probability that the next card he draws will be yellow?

Probability and combinatorics ### A population of N =16 scores has a mean of p = 20, After one score is removed from the population, the new mean is found to be $$\displaystyleμ={19}$$. What is the value of ine score that was removed? (Hint: Compare the val- ues for X before and after the score was removed.)

Probability and combinatorics ### The probability of rain in San Francisco on a given day is $$\displaystyle\frac{{1}}{{6}}$$. The probability of rain in Miami is $$\displaystyle\frac{{5}}{{6}}$$. Use two number cubes to find the simulated probability of rain in both cities.

Probability and combinatorics  