Problem Solving

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

On ANY individual toss, P(heads) = 1/2 and P(tails) = 1/2

P(heads 1st toss AND heads 2nd toss AND heads 3rd toss AND tails 4th toss AND tails 5th toss AND)
= P(heads 1st toss) x P(heads 2nd toss) x P(heads 3rd toss) x P(tails 4th toss) x P(tails 5th toss)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2
= 1/32

Answer: E

Cheers,
Brent

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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rsarashi wrote: ↑

Sat Sep 02, 2017 11:42 am

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

The probability that the first 3 flips are heads and last 2 flips are tails is:

P(HHHTT) = (1/2)^5 = 1/32.

Answer: E

rsarashi wrote: ↑

Sat Sep 02, 2017 11:42 am

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

The probability that the first 3 flips are heads and last 2 flips are tails is:

P(HHHTT) = (1/2)^5 = 1/32.

Answer: E