Hi, I have a few questions, I think I got pats a & b for question1, but questions 2 and 3 I'm not sure of.
1a.) Calculate the probability of at least one "6" in four rolls
1b.) Calculate the probability of obtaining at least one "double 6" in 24 rolls
2.)Two dice are rolled. Given that the faces show different numbers, what is the probability that one face is a "4"
3.) A coin comes up heads 3 times as often as tails. The coin is tossed three times. Let the random variable X= number of heads that appear. Write out the Probability Distribution Function of X.
For 1a I got 1-(5/6)^4 which equals a probability of 0.5177
and for 1b. I got 1-(35/36)^24 equals 0.4914
For 2, I drew a table of all possible outcomes when 2 dice are rolled. I pretty sure the answer would be 5/30 because out of all 36 possible outcomes, only 30 of the rolls involve non-repeated numbers, and only 5 of the 30 rolls contain a 4, but I'm not 100% positive.
as for 3, I'm not really sure where to begin
Thank you in advance!