Multiple choice

A box contains 3 blue and 7 yellow balls. 2 balls are drawn from the bag in succession without replacement .what is the probability that they are different colour ?

  1. 7/9

  2. 5/8

  3. 5/9

  4. 5/11

  5. 7/15
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

There are two favorable cases: (blue, yellow) and (yellow, blue). P(B,Y) = (3/10) × (7/9) = 21/90. P(Y,B) = (7/10) × (3/9) = 21/90. Total P(different colors) = 21/90 + 21/90 = 42/90 = 7/15. Alternatively, P(same color) = P(B,B) + P(Y,Y) = (3/10)(2/9) + (7/10)(6/9) = 6/90 + 42/90 = 48/90 = 8/15. Therefore, P(different) = 1 - 8/15 = 7/15.

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