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Manipal MET2023MathematicsProbability

An unbaised coin is tossed n times. If the probability of getting 5 heads is equal to the probability of getting 6 heads, then the probability of getting 3 heads is

Options

  1. A¹¹ C₅ ( 1 2 )^5
  2. B¹¹ C₆ ( 1 2 )^6
  3. C¹¹ C₃ ( 1 2 )¹¹
  4. D11 1024

Correct answer

C. ¹¹ C₃ ( 1 2 )¹¹

Step-by-step solution

The coin is tossed n times. Let x denotes the number of heads in n trials and it is given that p(x=5)=p(x=6) ^n C₅ ( 1 2 )^n= ^n C₆ ( 1 2 )^n n=11 p(x=3)= ¹¹ C₃ ( 1 2 )¹¹

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