math check probability

5. A bag contains 7 green marbles and 4 white marbles. You select a marble at random. What are the odds in favor of picking a green marble?

A. 7:11**?
B. 7:4
C. 4:7
D. 3:7 ------------------------------------ 6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk?

A. 11/156
B. 49/52
C. 2/39
D. 3/52

7. A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, and choose again. Find P(red, then blue).

A. 77/164
B. 19/41*
C. 90/1681
D. 45/41

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  1. #5. Nope
    The probability is 7/11, but the odds are 7:4

    That is, 7 chances for and 4 against.

    There are 147 without a star, so 9 with a star. So

    P(star) = 9/156 = 3/52

    total marbles: 41
    P(red) = 9/41
    P(blue) = 10/41
    P(red,blue) = 9/41 * 10/41 = 90/1681

    You can't just add the probabilities. If so, then by specifying enough drawings, you'd eventually add up enough fractions to get more than 1. Actually, by specifying more and more drawings, the chance of getting them ALL keeps getting smaller.

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