Consider a square board 3' x 3' (or picture  frame) hung on a wall. The board is  subdivided into 9 squares with equal size  (1' x 1'). A child throws a gooey blob at the  board that cleanly lands in one of the 9 squares with equal likelihood. If the squares are  numbered 1 to 9, (a) Find the prob that the blob lands in square  #1. (b) Find the prob that the blob lands in one of  the squares numbered 1 to 5,

If you flip a coin, there is a 1/2 chance you will receive a heads. If you flip a coin twice, you have to use the product rule to multiply each independent flip to find out what the odds of getting two heads in a row. (1/2 x 1/2=1/4.) By this rule, the odds of flipping a coin 13 times in a row twice and getting the exact same thing both times are 213. Mathematically, what are the chances that any two frog siblings will receive exactly the same complement of chromosomes due to random independent assortment (not counting random genetic recombination) Remember to add together the odds for both egg and sperm. What is this number for a human zygote? What does this tell you about the odds of being identical to one of your siblings, even without taking into account recombination (and not counting identical twins)?

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In tests of stopping distances for automobiles, those automobiles traveling at 30 miles per hour before the brakes are applied tend to travel distances that appear to be uniformly distributed between two points a and b. Suppose three automobiles are used in a test. Find the probability that exactly one of the three travels past the midpoint between a and b.

4846 pregnant women were tested to see if their babies had Down syndrome (D). The results of the test are given in the table. Use the values in the table to answer parts a-c. Blood Test Down POS NEG Total 50 11 61 D° 1045 3740 4785 Total 1095 3751 4846 a. Given that a test result is negative (NEG), what is the probability that the fetus actually has Down syndrome? P(D|NEG) = || (Do not round until the final answer. Then round to four decimal places as needed.) b. Given that the fetus has Down syndrome, what is the probability that the test result is negative? P(NEG|D) = (Do not round until the final answer. Then round to four decimal places as needed.) c. Is P(D|NEG) equal to P(NEG|D)? A. No, because P(NEG|D) deals with a much smaller pool of fetuses than P(D|NEG). B. Yes, because P(NEG|D) deals with a much smaller pool of fetuses than P(D|NEG). C. Yes, because P(NEG|D) deals with a much larger pool of fetuses than P(D|NEG). O D. No, because P(NEG|D) deals with a much larger pool of…

6. Choose 2 points (X, Y) uniformly at random from the circle. Find the expected area of the rectangle with opposite corners given by X and by Y.