GATE DA 2024 Set 1 — Question 12
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Probability & Statistics → Probability → Mutually Exclusive Events
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Question
Three fair coins are tossed independently. is the event that two or more tosses result in heads. is the event that two or more tosses result in tails.
What is the probability of the event ?
What is the probability of the event ?
Correct answer
(A) 0
Solution
Let be the number of heads and be the number of tails in 3 tosses. Note that .
Event : Two or more heads ().
Event : Two or more tails ().We are looking for , which corresponds to the event where AND .
Substituting , the condition for becomes .
So, requires AND , which is impossible.
Thus, , and .
Event : Two or more heads ().
Event : Two or more tails ().We are looking for , which corresponds to the event where AND .
Substituting , the condition for becomes .
So, requires AND , which is impossible.
Thus, , and .
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