The probability of obtaining at least two “SIX” in throwing a fair dice 4 time isa)425/432b)19/144c)13/144d)125/432Correct answer is option 'B'. Can you explain this answer?

Question

The probability of obtaining at least two &ldquo;SIX&rdquo; in throwing a fair dice 4 time isa)425/432b)19/144c)13/144d)125/432Correct answer is option 'B'. Can you explain this answer?

Answer

The probability of obtaining at least two tails in five flips of a fair coin can be calculated by subtracting the probability of obtaining zero or one tail from 1.

To calculate the probability of obtaining zero tails, we calculate the probability of obtaining all heads in five flips:
(1/2)^5 = 1/32

To calculate the probability of obtaining one tail, we calculate the probability of obtaining one tail and four heads in five flips. There are five possible positions for the tail, so we multiply the probability of getting a tail (1/2) by the probability of getting four heads (1/2)^4:
5 * (1/2) * (1/2)^4 = 5/32

To obtain the probability of obtaining at least two tails, we subtract the probabilities of obtaining zero or one tail from 1:
1 - (1/32 + 5/32) = 1 - 6/32 = 26/32 = 13/16

Therefore, the probability of obtaining at least two tails in five flips of a fair coin is 13/16.

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