Question 1196517: A bag contains five balls, numbered 1, 2, 3, 4 and 5. Another bag contains six balls numbered
1, 2, 3, 4, 5 and 6. One ball is drawn at random from each bag. Find the probability that
a) one ball is numbered 1 and the other 6,
b) both balls have an odd number,
(c) both balls have the same number,
(d) the sum of the numbers on the balls is 9.
Answer by greenestamps(13200)   (Show Source):
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There are 5 choices for the ball from the first bag and 6 choices for the ball from the second bag. So the number of possible draws is 5*6 = 30; that is the denominator of all the probability fractions.
(a) one ball is numbered 1, the other 6. The 6 had to come from the second bag, so the 1 had to come from the first.
Number of favorable outcomes: 1*1 = 1; probability 1/30
(b) both balls have an odd number. 3 possibilities from each bag.
Number of favorable outcomes: 3*3 = 9; probability 9/30
(c) both balls have the same number. That number can be 1, 2, 3, 4, or 5.
Number of favorable outcomes: 5; probability 5/30
(d) the sum of the numbers on the ball is 9. The combination can be 3+6, 4+5, or 5+4.
Number of favorable outcomes: 3; probability 3/30
ANSWERS:
(a) 1/30
(b) 9/30 = 3/10
(c) 5/30 = 1/6
(d) 3/30 = 1/10
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