1. Tardigrade
  2. Question
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  4. Consider two sets A = 1,2,3,4,5 and B = 1,2,3, ldots ldots, 9,10 . If Tina randomly selects two distinct numbers from set A and Reena randomly selects one number from set B, the probability that Reena's number is greater than the sum of the two number chosen by Tina, is

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Q. Consider two sets $A =\{1,2,3,4,5\}$ and $B =\{1,2,3, \ldots \ldots, 9,10\}$.
If Tina randomly selects two distinct numbers from set A and Reena randomly selects one number from set B, the probability that Reena's number is greater than the sum of the two number chosen by Tina, is

Probability - Part 2

Solution:

For Tina, $n ( S )={ }^5 C _2$
i.e. Two numbers selected are $12,13,14,15,23,24,25,34,35,45$ sum is $3,4,5,6,5,6,7,7,8,9$
Now for Reena, one number has to be selected so that sum is greater than the sum of the two numbers chosen by Tina
$\text { Required probability } =\frac{1}{10}\left(\frac{7+6+5+4+5+4+3+3+2+1}{10}\right) $
$=\frac{40}{100}=\frac{4}{10}=\frac{2}{5} $

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