rsarashi wrote:If a certain coin is flipped, the probability that the coin will land heads up is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
A) 3/5
B) 1/2
C) 1/5
D) 1/8
E) 1/32
OAE
I'm surprised that there is no answer as 5/16. This makes someone safe in case he/she does not get the question well.
Brent explained this one quite well.
Had the question been...
If a certain coin is flipped, the probability that the coin will land heads up is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on 3 flips and tail on 2 flips?
Unlike the original question in which the condition to get heads on the first 3 flips and tail to get on the last 2 flips, in the above-modified question, there is no such condition, thus, only important is to get 3 head out of 5 flips, be it in any order. A couple of instances HTHTH and HHTTH are valid.
Three instances of heads out of five instances is given by 5C3 = (5.4.3) / (1.2.3) = 10 ways.
Thus, the required probability = 5C3*[(1/2*1/2*1/2)*(1/2*1/2)] = 10*[1/2^5] = 5/16.
Hope this helps!
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