13. Let (, F, P) be a probability space and X a function from 2 to R. Explain when X is a random variable.
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- 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.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)Show that the probability of drawing a club at random from a standard deck of 52 playing cards is the same as the probability of drawing the ace of hearts at random from a set of four cards consisting of the aces of hearts, diamonds, clubs, and spades.
- A random number generator selects two integers from 1 to 30. What is the probability that both numbers are less than 12?Determine if the statement is true or false. If the statement is false, then correct it and make it true. The probability of a certain event is 0.If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on orange.