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# tango - [2 points Question 5a After you draw the ﬁrst...

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Math 210 Section 011: Test #4 NAME: This test has 6 pages . The points per page are 5, 4, 5, 5, 4, 5. [5 points] Question 1. How many integers in { 1 , 2 , 3 , . . . , 1000 } are not divisible by 2, 3, 5, or 7? 1

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[2 points] Question 2a. How many odd numbers in { 1000 , 1001 , 1002 , . . . , 9999 } have no repeated digits? [2 points] Question 2b. How many even numbers in { 1000 , 1001 , 1002 , . . . , 9999 } have no repeated digits? 2
[5 points] Question 3. How many permutations of the letters a, b, c, d, e, f, g have either two or three letters between a and b ? 3

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[5 points] Question 4. You roll 3 balanced six-sided dice. What’s the probability that the total is at most 16? 4
In both Question 5a and Question 5b , you have a basket that contains 5 red balls, 4 white balls, and 3 blue balls. You randomly draw a ball from the basket so that each of the 12 balls is equally likely.

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Unformatted text preview: [2 points] Question 5a. After you draw the ﬁrst ball, you replace it in the basket, and you then make a second random draw of one of the 12 balls. What’s the probability that you get the same color on the ﬁrst and second draw? [2 points] Question 5b. After you draw the ﬁrst ball, you don’t replace it in the basket, and you then make a second random draw of one of the 11 remaining balls. What’s the probability that you get the same color on the ﬁrst and second draw? 5 [5 points] Question 6. You have an unbalanced coin where the probability of heads is 2/3 and the probability of tails is 1/3. You toss the coin 5 times. What’s the probability that the number of heads is odd? 6...
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