The students at a university are classified by a 0 for freshman, a 1 for sophomores, a 2 for juniors, a 3 for seniors, and a 4 for graduate students. There are two extra scholarships to assign, so an administrator randomly selects from a box with only the numbers 0, 1, 2, 3, and 4 to choose the class of the first recipient. She then puts the number back into the box and randomly selects a number for the class of the second recipient. Find the sample space , and then find the probability of the following events: (a) An odd number is chosen first and an even number is chosen second. ( Note: 0 is considered an even number.) (b) The sum of the two numbers selected is greater than 4. (c) For both selections, an even number is drawn. (d) The sum of the two numbers selected is odd. (e) The same number is drawn twice.
The students at a university are classified by a 0 for freshman, a 1 for sophomores, a 2 for juniors, a 3 for seniors, and a 4 for graduate students. There are two extra scholarships to assign, so an administrator randomly selects from a box with only the numbers 0, 1, 2, 3, and 4 to choose the class of the first recipient. She then puts the number back into the box and randomly selects a number for the class of the second recipient. Find the sample space , and then find the probability of the following events: (a) An odd number is chosen first and an even number is chosen second. ( Note: 0 is considered an even number.) (b) The sum of the two numbers selected is greater than 4. (c) For both selections, an even number is drawn. (d) The sum of the two numbers selected is odd. (e) The same number is drawn twice.
Solution Summary: The author explains that the probability of an odd number being chosen first and an even number choosing second is 625.
The students at a university are classified by a 0 for freshman, a 1 for sophomores, a 2 for juniors, a 3 for seniors, and a 4 for graduate students. There are two extra scholarships to assign, so an administrator randomly selects from a box with only the numbers 0, 1, 2, 3, and 4 to choose the class of the first recipient. She then puts the number back into the box and randomly selects a number for the class of the second recipient. Find the sample space, and then find the probability of the following events:
(a) An odd number is chosen first and an even number is chosen second. (Note: 0 is considered an even number.)
(b) The sum of the two numbers selected is greater than 4.
(c) For both selections, an even number is drawn.
(d) The sum of the two numbers selected is odd.
(e) The same number is drawn twice.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
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