A jar contains 8 red marbles numbered 1 to 8 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability that the marble is blue or odd-numbered.

66.6%

Step-by-step explanation:

The probability that it is blue or odd, would be the quotient between the marbles of these characteristics and the total number of marbles.

Now, we know that there are four blue marbles altogether. The odd ones, in the case of the red ones since there are eight, are the marbles 1,3,5,7 and in the blue ones the odd ones are not counted because they are already included as blue; therefore there are a total of four odd marbles. In total, between odd and blue there are eight marbles.

Which means that the probability is as follows, knowing that there are a total of 12 marbles:

8/12 = 0.666, that is, there is 66.6% chance that the marble that is drawn is blue or an odd number.

find the magnitude of the trig term  

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find the upper bound of the range.

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step-by-step explanation: