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A fair coin is tossed a fixed number of times. If the probability of getting 4 heads is equal to the probability of getting 7 heads, then the probability of getting 2 heads is
  • a)
    55/2048
  • b)
    3/4096
  • c)
    1/1024
  • d)
    3/1024
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A fair coin is tossed a fixed number of times. If the probability of g...
Given, probability of getting 4 heads = probability of getting 7 heads
Let the number of tosses be n. Then,
Probability of getting 4 heads = Probability of getting (n-4) tails = (1/2)^n * nC4
Probability of getting 7 heads = Probability of getting (n-7) tails = (1/2)^n * nC7
Equating the two probabilities, we get
nC4 = nC7/35
Solving this equation, we get n = 11
So, the number of tosses is 11.

Now, we need to find the probability of getting 2 heads.
Probability of getting 2 heads = Probability of getting (11-2) tails = (1/2)^11 * nC2
= (1/2)^11 * 55
= 55/2048

Therefore, the correct option is A) 55/2048.
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Community Answer
A fair coin is tossed a fixed number of times. If the probability of g...
“n” be the fixed number of times a coin be tossed.

Given that the probability of getting 7heads is equal to the probability of getting 4 heads.

nC7 (½)7(½)n-7 = nC4 (½)4 (½)n-4

nC7 = nC4

Therefore, n= 11

Hence, the probability of getting 2 heads = 11C2 (½)2(½)11-2

= 11C2 (½)11

= 55/2048
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A fair coin is tossed a fixed number of times. If the probability of getting 4 heads is equal to the probability of getting 7 heads, then the probability of getting 2 heads isa)55/2048b)3/4096c)1/1024d)3/1024Correct answer is option 'A'. Can you explain this answer?
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