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Two different dice are thrown together. Find the probability that the numbers obtained have$( i)$ even sum, and
$( ii)$ even product.
Given: Two different dice are thrown together.
To do: To Find the probability that the numbers obtained have
$( i)$ even sum, and
$( ii)$ even product
Solution:
Two dice are thrown together total possible outcomes $=6\times 6=36$
Sum of outcomes is even This can be possible when Both outcomes are even Both outcomes are odd
For both outcomes to be Even number of cases\ $= 3\times 3\ =9$
Similarly Both outcomes odd $=9$ cases
Total favourable cases $=9+9=18$
Probability of even sum $=\frac{18}{36} =\frac{1}{2}$
$( i)$. Product of outcomes is even
This is possible when
Both outcomes are even
First outcome even & the other odd
first outcome odd & the other even
Number of cases where both outcomes are even$=9$
Number of cases for first outcome odd $=9$
No. of cases for first outcome odd and the other$=9$
Total favourable outcomes$=9+9+9=27$
Probability$=\frac{27}{36} =\frac{3}{4}$.
Updated on: 10-Oct-2022
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