What is the probability that your 10-toss sequence is either all heads or all tails?You toss a balanced coin 10 times and write down the resulting...

Interpreting  a balanced coin to be an unbiased one , the probability of showing head or tail in a single toss is (1/2) each.Or P(H)=P(T) =(1/2).

If A and B are two independent events, then P(AB) = P(A)P(B).

Therefore, probability of getting 10 heads in 10 tosses (tosses being independent) = P(HHHHHHHHHH) = (1/2)(1/2)... 10 factors=(1/2)^10.

Similarly Probability of getting 10 tails= P(TTTTTTTTTT)=(1/2)^10.

Since both events are exclusive, the probability of getting 10 heads or 10 tails is equal to the sum of the the individual probabilities = P(HHHHHHHHHH)+P(TTTTTTTTTT) = (1/2)^10+(1/2)^10 = 2(1/2)^10 = 2^(-9) =1/512 = 1.953125*10^(-3)