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On three consecutive flips of a coin, what is the probability that all
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20 Jan 2022, 06:14
20 Jan 2022, 06:14
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On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
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Re: On three consecutive flips of a coin, what is the probability that all
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20 Jan 2022, 07:02
20 Jan 2022, 07:02
Carcass wrote:
On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
APPROACH #1
P(3 identical flips) = P(1st flip is ANY side AND 2nd flip matches 1st flip AND 3rd flip matches 1st flip)
= P(1st flip is ANY side) x P(2nd flip matches 1st flip) x P(3rd flip matches 1st flip)
= 1 x 1/2 x 1/2
= 1/4
Answer: C
APPROACH #2
P(3 identical flips) = P(3 heads in a row OR 3 tails in a row)
= P(3 heads in a row) + P(3 tails in a row)
= P(1st flip is heads AND 2nd flip is heads AND 3rd flip is heads) + P(1st flip is tails AND 2nd flip is tails AND 3rd flip is tails)
= [P(1st flip is heads) x P(2nd flip is heads) x P(3rd flip is heads)] + [P(1st flip is tails) x P(2nd flip is tails) x P(3rd flip is tails)]
= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]
1/8 + 1/8
= 1/4
Answer: C
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Re: On three consecutive flips of a coin, what is the probability that all
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18 Oct 2022, 10:04
18 Oct 2022, 10:04
1
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
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
