NIMCET Probability Critical Thinking Previous Year Questions (PYQs)
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Showing 4 questions
In a class of 100 students, 55 passed in Mathematics and 67 passed in Physics.The number of students who passed in Physics only is:
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4
Solution
Use the formula:
$\text{Physics only} = n(P) - n(M \cap P)$
First find $n(M \cap P$) using:
$n(M) + n(P) - n(M \cap P) = 100$
So:
$55 + 67 - n(M \cap P) = 100$
$122 - n(M \cap P) = 100$
$n(M \cap P) = 22$
Now:
$\text{Physics only} = 67 - 22 = 45$
Survey: $63%$ like cheese, $76%$ like apples. If $x%$ like both?
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Solution
Using inclusion–exclusion:
$63 + 76 - x \le 100$
$139 - x \le 100$
$x \ge 39$
Max value of $x$ cannot exceed minimum of both percentages
→ $x \le 63$
Thus $39 \le x \le 63$.
A six-faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is
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Solution
Let $P(\text{even})=p$ and $P(\text{odd})=3p$
$p+3p=1 \Rightarrow p=\dfrac14$
So
$P(\text{even})=\dfrac14,\quad P(\text{odd})=\dfrac34$
Sum is even when both outcomes are even or both are odd.
$P=\left(\dfrac14\right)^2+\left(\dfrac34\right)^2=\dfrac1{16}+\dfrac9{16}=\dfrac{10}{16}=\dfrac58$
Answer: $\boxed{\dfrac58}$
A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is
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Solution
TATANAGAR has $2$ occurrences of TA
CALCUTTA has $3$ occurrences of TA
Total occurrences $=5$
Required probability
$=\dfrac{3}{5}$
This is not listed.
Answer: $\boxed{\text{None of these}}$
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