A balanced coin is tossed thrice. If the first two tosses have resulte

1.	A balanced coin is tossed thrice. If the first two tosses have resulted in tail, find the probability that tail appears on the coin In all the three trials.
Answer» A = Event that in the first trial tall is obtained. B = Event that in the second trial tail is obtained on the coin. ∴ P(A) = \(\frac{1}{2}\) P(B) = \(\frac{1}{2}\) C = Event that in the first two trials tail is obtained on the coin. ∴ P(C) = P(A) ∙ P(B) = \(\frac{1}{2}×\frac{1}{2}\) = \(\frac{1}{4}\) D\|C = Event that tall appears on the in all three trials if the first two trials resulted in tail ∴ P(D\|C) = \(\frac{P(D∩C)}{P(C)}\) D ∩ C = Event that in the first two trails and In the third trial tail is obtained on the coin ∴ P(D ∩ C) = P(D) ∙ P(C) = \(\frac{1}{2}×\frac{1}{4}\) = \(\frac{1}{8}\) Now, P(D\|C) = \(\frac{P(D∩C)}{P(C)} = \frac{\frac{1}{8}}{\frac{1}{4}}\) = \(\frac{1}{8}×\frac{4}{1}=\frac{1}{2}\)

A balanced coin is tossed thrice. If the first two tosses have resulted in tail, find the probability that tail appears on the coin In all the three trials.

Answer»

A = Event that in the first trial tall is obtained.
B = Event that in the second trial tail is obtained on the coin.

∴ P(A) = \(\frac{1}{2}\) P(B) = \(\frac{1}{2}\)

C = Event that in the first two trials tail is obtained on the coin.

∴ P(C) = P(A) ∙ P(B)

= \(\frac{1}{2}×\frac{1}{2}\)

= \(\frac{1}{4}\)

D|C = Event that tall appears on the in all three trials if the first two trials resulted in tail

∴ P(D|C) = \(\frac{P(D∩C)}{P(C)}\)

D ∩ C = Event that in the first two trails and In the third trial tail is obtained on the coin

∴ P(D ∩ C) = P(D) ∙ P(C)

= \(\frac{1}{2}×\frac{1}{4}\)

= \(\frac{1}{8}\)

Now, P(D|C) = \(\frac{P(D∩C)}{P(C)} = \frac{\frac{1}{8}}{\frac{1}{4}}\)

= \(\frac{1}{8}×\frac{4}{1}=\frac{1}{2}\)

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