A coin is tossed until two"heads" have been obtained or four tosses have been made, whichever comes first. List the elements of the sample space of this experiment.
A box contains balls that are identical except for color. Initially the box contains one red and two green balls. A ball is drawn at random from the box and then put back in the box. If the chosen ball was red, three red balls, one green ball, and two blue balls are added to the box. If the chosen ball was green, three green balls and one blue ball are added to the box. After the extra balls are added, a ball is drawn at random from the box. Determine the probability that this ball is red.
A box contains balls that are identical except for color. Initially the box contains three blue and two green balls. A ball is drawn at random from the box and its color is observed. This first ball is then put back in the box, and then four balls of the other color are added to the box. After the extra balls are added, a ball is drawn at random from the box. Given that this ball is blue, determine the probability that the first ball drawn from the box was green.
A certain measured voltage is a Gaussian random variable with mean = 50 V and standard deviation = 5 V. Determine the probability that the
measured voltage will be between 42 V and 52 V.