GATE EE 2015 Set 2 — Question 37
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Engineering Mathematics → Probability → Joint Probability & Independence
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Question
Two coins and are tossed. The 4 joint events have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where represents head and represents tail. Which one of the following is TRUE?
Correct answer
(D) The coin tosses are dependent.
Solution
Let the joint probabilities be given as:
First, calculate the marginal probabilities for each coin:
For coin :
Since , coin is not fair.For coin :
Since , coin is not fair.Now, check for independence:
If the tosses were independent, .
Since , the events are dependent.Therefore, statement (D) is the only true statement.
First, calculate the marginal probabilities for each coin:
For coin :
Since , coin is not fair.For coin :
Since , coin is not fair.Now, check for independence:
If the tosses were independent, .
Since , the events are dependent.Therefore, statement (D) is the only true statement.
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