GATE 2020 ME (ME2) – Question 46
A fair coin is tossed 20 times. Find probability that heads appear exactly 4 times in the first 10 tosses and tails exactly 4 times in the next 10 tosses, to three decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: .041 to .043
Explanation
The disjoint blocks are independent. Each requested count has probability $\binom{10}4/2^{10}=210/1024$. Multiplying gives(210/1024)²=0.0420570, rounded **0.042**. The second count is tails, but symmetry gives the same binomial probability.