On three consecutive flips of a coin, what is the probabilit

Why isn't "B" the answer?

probability for head = \(1/2\)
similarly probability for tails = \(1/2\)

case 1: all 3 times = head
in that case
probability \(= 1/2*1/2*1/2 = 1/8\)

case 2 : all tails then again probability will be \(1/8\)

so total probability will be \(1/8+1/8 = 1/4\)

hope it helps

If they had to all three be heads, then the calculation would be 1/2 * 1/2 * 1/2 = 1/8

In addition to getting the chosen outcome if we get three heads, we know that also we have success if the the three are all tails. So right there you know that the probability is greater than the 1/8 for three heads.

How much greater?

Well we have success if they are all heads. The probability of that is 1/8.

We also have success if they are all tails. The probability of that is also 1/8.

So we add the two together for the total probability of success, which is 1/8 + 1/8 = 1/4, choose .

TL;DR

HHH or TTT
Possible Cases: 2
Total Cases: 2^3 = 8
P = 2/8 = 1/4

or P = 1 * 1/2 * 1/2 = 1/4
ANSWER: C

Veritas Prep Official Solution

The trap answer here is 1/8 – you might look at this as a 1/2 probability on the first flip, then a 1/2 on the second, and a 1/2 on the third for a 1/8 probability, but remember – in this case the result of the first flip doesn’t have to be one or the other. Your job is just to match whatever the first result was on the next two. If the first was heads, then you need heads next (a 1/2 chance) and heads again (a 1/2 chance). And if it were tails, then you need tails (1/2) then tails (1/2). But because “any match will do” and you don’t care that it’s a specific match – the question doesn’t specify all heads or all tails, just “all of one of them” – your probability doubles because you’re not concerned about the result of the first event, you’re only concerned about matching whatever that result was.

General Tips

Credit: Veritas Prep

So for probability questions that ask about pairs or matches, remember:

1) Check whether you need a *specific* pair/match or not.

2) If you don’t need a specific pair, but “any pair will do,” then the probability of the first result is 100% – something will happen.

3) If you need to guess, keep in mind that if it’s an unspecified pair/match, it’s almost certain that one of the trap answers will be a smaller number than the correct answer (in the above case, 1/8 is a trap and 1/4 is correct), so you can confidently rule out the smallest number and use number properties to try to eliminate another 1-2 answers.

Probability of getting heads or tails on the first coin: 1

Probability of getting a matching result on the second coin: 1/2

Probability of getting a matching result on the third coin: 1/2

1 * 1/2 * 1/2 = 1/4

We need to find On three consecutive flips of a coin, what is the probability that all three produce the same result?

Coin is tossed 3 times => Total number of cases = \(2^3\) = 8

Lets solve the problem using two methods

Method 1:

Out of the 8 cases there are only two cases in which all the outcomes are same. HHH and TTT.

=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)

So, Answer will be C

Method 2:

Let's find out the number of cases.
In the first toss we can get anything out of head or tail in 2 ways
In second toss we need to get the same value (head or tail) as we got in the first toss => 1 way
In third toss we need to get the same value (head or tail) as we got in the second toss => 1 way

=> Total number of ways = 2*1*1 = 2 ways

=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

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