A and B toss a fair coin each simultaneously | vedclass

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(A) For each toss,there are $4$ possible outcomes for $A$ and $B$ together: $(H, H), (T, H), (H, T), (T, T)$.Since the coins are fair,each outcome has

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$(\frac{3}{4})^{50}$

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(A) For each toss,there are $4$ possible outcomes for $A$ and $B$ together: $(H, H), (T, H), (H, T), (T, T)$.Since the coins are fair,each outcome has a probability of $\frac{1}{4}$.The event that both do not get a tail at the same toss means we exclude the outcome $(T, T)$.Thus,for a single toss,there are $3$ favorable outcomes: $(H, H), (T, H), (H, T)$.The probability of not getting a tail at the same time in a single toss is $P = \frac{3}{4}$.Since they toss the coins $50$ times independently,the probability that this happens in all $50$ tosses is $(\frac{3}{4})^{50}$.

List-$A$	List-$B$
$(I)$ $A, B$ are mutually exclusive events	$(i)$ $P(A \cap B) = P(B) - P(\bar{A})$
$(II)$ $A, B$ are independent events	$(ii)$ $P(A) \leq P(B)$
$(III)$ $A \cap B = A$	$(iii)$ $P(\frac{\bar{A}}{B}) = 1 - P(A)$
$(IV)$ $A \cup B = S$	$(iv)$ $P(A \cup B) = P(A) + P(B)$
	$(v)$ $P(A) + P(B) = 2$

$A$ and $B$ toss a fair coin each simultaneously $50$ times. The probability that both of them will not get tail at the same toss is

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