JEE MAIN - Mathematics (2022 - 28th June Morning Shift - No. 11)
The probability, that in a randomly selected 3-digit number at least two digits are odd, is :
$${{19} \over {36}}$$
$${{15} \over {36}}$$
$${{13} \over {36}}$$
$${{23} \over {36}}$$
Explanation
At least two digits are odd = exactly two digits are odd + exactly there 3 digits
are odd
For exactly three digits are odd
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For exactly two digits odd :
If 0 is used then $: 2 \times 5 \times 5=50$
If 0 is not used then : ${ }^3 \mathrm{C}_1 \times 4 \times 5 \times 5=300$
Required Probability $=\frac{475}{900}=\frac{19}{36}$
For exactly three digits are odd
For exactly two digits odd :
If 0 is used then $: 2 \times 5 \times 5=50$
If 0 is not used then : ${ }^3 \mathrm{C}_1 \times 4 \times 5 \times 5=300$
Required Probability $=\frac{475}{900}=\frac{19}{36}$
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