Player A will shut out (win by a score of 21-0) player B in a game of racquetball with probability P = 1+P 2 р 1-p+p² 21 where p denotes the probability A will win any specific rally (independent of the server). (See [Keller, J], p. 267.) Determine, to within 10-3, the minimal value of p that will ensure that A will shut out B in at least half the matches they play. (Use secant or bisection cr both)

Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.

The following table shows frequencies for red-green color blindness, where M represents person is male and C represents person is colour-blind. Use this table to find the following probabilities. See Exercise 86, Section 12.2 M M Totals C 0.035 0.004 0.039 C 0.452 0.509 0.961 Totals 0.487 0.513 1.000 a. P(M) b. P(C) c. P(MC) d. P(MC) e. P(M|C) f. P(C|M) g. P(M|C) h. Are the events C and M, described above, dependent? What does this mean?

If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)