GATE 2024 ST – Question 18

Probability · Events and Conditional Probability · 1 mark · Multiple choice

Independent fair red and blue dice are thrown once. A:red die is 5 or 6; B:sum is 7; C:sum is 8. Which holds?

A,B independent and A,C independent
A,B independent but A,C dependent
A,C independent but A,B dependent
Both pairs dependent

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Show answer and explanation

Correct answer: (B) A,B independent but A,C dependent

Explanation

P A=1/3,P B=6/36=1/6, and A∩B contains (5,2),(6,1), probability 2/36=1/18=P A·P B. P C=5/36, while A∩C contains (5,3),(6,2), probability 2/36≠5/108=P A·P C. **B**.

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