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Chapter 4: Q. 4.39 (page 166)

A ball is drawn from an urn containing 3white and 3black balls. After the ball is drawn, it is replaced and another ball is drawn. This process goes on indefinitely. What is the probability that the first 4balls drawn, exactly2 are white?

Short Answer

Expert verified

The probability that of the first 4balls drawn, exactly 2are white is38.

Step by step solution

01

Given Information

Given in the question that a ball is drawn from an urn containing 3white and 3black balls. After the ball is drawn, it is replaced and another ball is drawn.

02

Solution of the Problem

Probability of drawing white ball=36

=12

Probability of drawing a black ball =36

=12

Number of ways of choosing 2white 4draws =42

=6ways

Desired probability=6×122×122

=38.

03

Final Answer

The probability that of the first 4 balls drawn, exactly 2are white is 38.

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Most popular questions from this chapter

Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always bets that the outcome will be one of the numbers 1 through 12, what is the probability that

  1. Smith will lose his first 5 bets;
  2. his first win will occur on his fourth bet?

It is known that diskettes produced by a certain company will be defective with probability .01, independently of one another. The company sells the diskettes in packages of size 10and offers a money-back guarantee that at most1of the diskettes in the package will be defective. The guarantee is that the customer can return the entire package of 10 diskettes if he or she finds more than 1 defective diskette in it. If someone buys 3 packages, what is the probability that he or she will return exactly 1 of them?

A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability .3,and his second will lead independently to a sale with probability .6. Any sale made is equally likely to be either for the deluxe model, which costs \(1000, or the standard model, which costs \)500. Determine the probability mass function of X, the total dollar value of all sales

4.20. A gambling book recommends the following "winning strategy" for the game of roulette: Bet \(1on red. If red appears (which has probability 1838), then take the \)1profit and quit. If red does not appear and you lose this bet (which has probability 2038of occurring), make additional $1bets on red on each of the next two spins of the roulette wheel and then quit. Let Xdenote your winnings when you quit.

(a) Find P{X>0}.

(b) Are you convinced that the strategy is indeed a "winning" strategy? Explain your answer!

(c) Find E[X].

For a hypergeometric random variable, determine

P{X=k+1}/P{X=k}
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