Question

On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. if you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? explain.

Answer 1

Supposing that the coin is unbiased, and that landing on head and tail are exhaustive events.
So, P (first toss resulting in head) = 1/2and P (second toss resulting in a tail) = 1/2.
The two are independent events, necessary probability (their product) is 1/4.
Another way to see it as: 
Possible outcomes: HH, HT, TH and TT, each with equal probability. Hence, ¼The answer is no because all have an equal probability and the possible outcomes for this can be HH or HT.