A pink-flowering plant is of genotype RW. If two such plants are crossed, we obtain a red plant (RR) with probability .25, a pink plant (RW or WR) with probability .50, and a white plant (WW) with probability .25, as shown in the table. What is the expected number of W genes present in a crossing of this type?

$$\begin{matrix} \text{Number of W Genes Present} & \text{}\\ \text{}{x_{i}} & \text{}{p_{i}}\\ \text{0} & \text{.25}\\ \text{1} & \text{.50}\\ \text{2} & \text{.25}\\ \end{matrix}$$

An automobile manufacturer produces 37% of its cars at plant A. If 5% of the cars manufactured at plant A have defective emission control devices, what is the probability that one of this manufacturer's cars was manufactured at plant A and ha s a defective emission control device?

When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW). If two pink snapdragons are crossed, what is the probability that the offspring will be

pink?

In four-o'clocks, the allele for red flowers is incompletely dominant over the allele for white flowers, so heterozygotes have pink flowers. What ratios of flower colors would you expect among the offspring of the following crosses: (a) pink $\times$ pink, (b) white $\times$ pink, (c) red $\times$ red, (d) red $\times$ pink, (e) white $\times$ white, and (f) red $\times$ white? If you specifically wanted to produce pink flowers, which of these crosses would be most efficient?

A television advertising campaign is conducted during the football season to promote a well-known brand X shaving cream. For each of several weeks, a survey is made, and it is found that each week, 80% of those using brand X continue to use it and 20% switch to another brand. It is also found that of those not using brand X, 20% switch to brand X while the other 80% continue using another brand. (A) Draw a transition diagram. (B) Write the transition matrix. (C) If 20% of the people are using brand X at the start of the advertising campaign, what percentage will be using it 1 week later? 2 weeks later?

Draw a Punnett Square to show the possible results of two inbred mice with pure recessive genes for tail length (tt/tt). Then draw a Punnett Square to show the possible results of two outbred mice. One has dominant genes for a long tail (Tt) and the other has recessive genes for a sh on tail (tt).

A game has an expected value to you of $100. It costs$100 to play, but if you win, you receive $100,000 (including your$100 bet) for a net gain of $99,900. What is the probability of winning? Would you play this game? Discuss the factors that would influence your decision.

An urn contains 2 one-dollar bills, 1 five-dollar bill, and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. (A) What is the probability of winning $16? (B) What is the probability of winning all bills in the urn? (C) What is the probability of the game stopping at the second draw?

A card is drawn from a standard 52-card deck. If the card is a king, you win $10; otherwise, you lose$1. What is the expected value of the game?

After careful testing and analysis, an oil company is considering drilling in two different sites. It is estimated that site A will net $30 million if successful (probability .2) and lose$3 million if not (probability .8); site B will net $70 million if successful (probability .1) and lose$4 million if not (probability .9). Which site should the company choose according to the expected return for each site?

By transforming to polar coordinates, show that the double integral $\iint \frac{\left(x^{2}+y^{2}\right)^{2}}{(x y)^{2}} \mathrm{d} x \mathrm{d} y$ taken over the area common to the two circles $x^{2}+y^{2}=a x \text { and } x^{2}+y^{2}=b y$ is ab.

Five thousand tickets are sold at $1 each for a charity raffle. Tickets will be drawn at random and monetary prizes awarded as follows: 1 prize of$500; 3 prizes of $100, 5 prizes of$20, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?

Five thousand tickets are sold at $\$1$ each for a charity raffle. Tickets will be drawn at random and monetary prizes awarded as follows: $1$ prize of $\$500$; $3$ prizes of $\$100$, $5$ prizes of $\$20$, and $20$ prizes of $\$5$. What is the expected value of this raffle if you buy $1$ ticket?

Illustrate in the form of a Punnett square the results of crossing a pink-flowering four o'clock with a white-flowering four o'clock.