JEE Main 2016MathematicsProbabilityMediumMCQ

JEE Main 2016 — Probability Question with Solution

JEE Main 2016 (03 Apr)

Question

Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?

Choose an option

Show full solutionCorrect option: B
Correct answer
BE1, E2 and E3 are independent

Step-by-step explanation

E1→A show up 4

E2→B shows up 2

E3→  Sum is odd (i.e., even + odd or odd + even)

PE1=66.6=16

PE2=66.6=16

PE3=3.36.6+3.36.6=24=12

PE1∩E2=16.6=PE1 . PE2

⇒ E1 & E2 are independent

PE1∩E3=1.36.6=PE1 . PE3

⇒ E1 & E3 are independent

PE2∩E3=1.36.6=112=PE2 . PE3

⇒ E2 & E3 are independent

PE1∩E2∩E3=0 ≠P(E1)×P(E2)×P(E3) 

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About this question

This is a previous-year question from JEE Main 2016, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.