a fair coin is tossed in the air 4 times. if the coin lands heads up the first three tosses, what is the probability the coin will land heads up the fourth toss?
I think it is 1/2 because the coin has 2 sides and 50% it will land on heads.
My friend thinks it is 1/16, since each toss is 1/2, so 1/2 *1/2*1/2*1/2=1/16 since you mult each toss
Am I correct or is my friend?
Thanks for the help
You're right. Each toss is independent of other tosses. Therefore each toss has a 1/2 chance of landing heads up.
Thank you!!!
You're welcome.
Your friend is correct. The probability of the coin landing heads up on each individual toss is indeed 1/2. However, when you want to calculate the probability of multiple independent events occurring together, you need to multiply their individual probabilities.
In this case, since there are 4 tosses and each has a 1/2 probability of landing heads up, you need to multiply 1/2 by itself four times. So, the correct calculation would be (1/2) * (1/2) * (1/2) * (1/2) = 1/16.
Therefore, the probability that the coin will land heads up on the fourth toss, given that it landed heads up on the first three tosses, is indeed 1/16.