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A fair coin is tossed independently five times. The probability of the event "the number of times tails show up is less than the number of times heads show up” is
  • a)
    1/5
  • b)
    1/4
  • c)
    1/3
  • d)
    1/2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A fair coin is tossed independently five times. The probability of the...
Coin is tossed 5 times
P(number of tails < number="" of="" />
= p5x & oT or 4x & IT or 3x & 2T
= p(exactly 5 neads) + p(exactly 4 heads)
+ p(exactly 3 heads)
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Most Upvoted Answer
A fair coin is tossed independently five times. The probability of the...
The probability of getting exactly 3 heads in 5 coin tosses can be calculated using the binomial probability formula.

The formula for the probability of getting exactly k successes in n independent Bernoulli trials, each with probability of success p, is given by:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In this case, we want to calculate the probability of getting exactly 3 heads (k = 3) in 5 coin tosses (n = 5), and the probability of getting a head on any single toss is 0.5 (p = 0.5).

Using the formula, we have:

P(X = 3) = (5 choose 3) * (0.5)^3 * (1-0.5)^(5-3)
= 10 * 0.125 * 0.25
= 0.3125

Therefore, the probability of getting exactly 3 heads in 5 coin tosses is 0.3125 or 31.25%.
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A fair coin is tossed independently five times. The probability of the event "the number of times tails show up is less than the number of times heads show up” isa)1/5b)1/4c)1/3d)1/2Correct answer is option 'D'. Can you explain this answer?
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