Zach said he would help Stuart clean his room if Stuart flips a coin 4 times and gets heads all 4 times. What is the probability that Stuart will flip a coin 4 times and get heads all 4 times?
Choices-
A- 1/16
B- 1/8
C- 1/4
D- 1/2
I am super confused I think it is C but I don't know can someone help me or guide me. Thanks!
each flip is an independent event
... with the probability of heads being 1/2
the probability of multiple independent events is
... the product of their individual probabilities
So C?
I mean D.
D. yes
I think…?
wait no sorry its 4 times not just once
1/2 * 1/2 * 1/2 * 1/2 = ?
that's 2
To find the probability of flipping a coin 4 times and getting heads all 4 times, we can use the concept of independent events. Assuming the coin is fair (i.e., has an equal chance of landing on heads or tails), the probability of getting heads on any given flip is 1/2.
Since each flip is independent of the others, the probability of getting heads 4 times in a row is the product of the probabilities of each individual flip. So, the probability can be calculated as follows:
Probability of getting heads on the first flip = 1/2
Probability of getting heads on the second flip = 1/2
Probability of getting heads on the third flip = 1/2
Probability of getting heads on the fourth flip = 1/2
To find the overall probability, we multiply these individual probabilities together:
(1/2) * (1/2) * (1/2) * (1/2) = 1/16
Therefore, the probability that Stuart will flip a coin 4 times and get heads all 4 times is 1/16. So, the correct choice is A.