I'm having a little trouble understanding when we would use conditional probability in the question below.
I was thinking since we are already given that there are at least 6 tails, we wouldn't need to consider that probability, and only calculate the probability of tossing exactly 1 tail (and hence 1 head) in 6th and 7th tosses, which would give 1/2 since the possible outcomes are TH, HT, TT, HH, and 2/4 outcomes have exactly one tail. Could someone please verify if that approach is right or if we'd need to use conditional probability in this case?
Assume that the outcome of either heads or tails is equally likely in coin tosses, and each coin toss event occurs independently. You toss the coin exactly 8 times. Given that at least 6 of those tosses resulted in tails, what is the probability that exactly 7 tosses were tails?