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When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
29 Oct 2012, 01:17
Kudos
Bookmarks
When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
We need the proability of HHHTTT (any combination of this): \(P=\frac{6!}{3!3!}*(\frac{1}{2})^6=\frac{20}{64}=\frac{5}{16}\). We are multiplying by \(\frac{6!}{3!3!}\) since HHHTTT scenario can occur in several ways: HHHTT, THHHTT, TTHHHT, ... basically the number of permutations of 6 letters HHHTTT, out of which 3 H's and T's are identical (\(\frac{6!}{3!3!}\));
Answer: C.
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Probability chapter of out Math Book:
math-probability-87244.html
Hope it helps.
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
We need the proability of HHHTTT (any combination of this): \(P=\frac{6!}{3!3!}*(\frac{1}{2})^6=\frac{20}{64}=\frac{5}{16}\). We are multiplying by \(\frac{6!}{3!3!}\) since HHHTTT scenario can occur in several ways: HHHTT, THHHTT, TTHHHT, ... basically the number of permutations of 6 letters HHHTTT, out of which 3 H's and T's are identical (\(\frac{6!}{3!3!}\));
Answer: C.
Check similar questions to practice:
what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html
there-is-a-90-chance-that-a-registered-voter-in-burghtown-56812.html
combination-ps-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html
if-a-certain-coin-is-flipped-the-probability-that-the-coin-58357.html
what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html
a-store-buys-10-bottles-of-alcohol-including-7-bottles-of-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html
a-gumball-machine-contains-7-blue-5-green-and-4-red-141079.html
a-basket-contains-3-blue-3-red-and-3-yellow-marbles-if-55673.html
there-are-10-solid-colored-balls-in-a-box-including-1-green-135103.html
when-a-random-experiment-is-conducted-the-probability-that-89835.html
if-the-probability-of-sita-getting-selected-to-a-school-is-130643.html
in-a-multiple-choice-test-comprising-5-questions-each-with-136936.html
if-a-certain-coin-is-flipped-the-probability-that-the-coin-58357.html
Probability chapter of out Math Book:
math-probability-87244.html
Hope it helps.
28 Oct 2012, 22:27
Kudos
Bookmarks
kapsycumm
When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
Required series is HHHTTT = \((\frac{1}{2})^6\) = \(1/64\)
This combination can occur in \(\frac{6!}{3!*3!}\) ways. ie 20 ways
So answer = \(\frac{1}{64}*20\) \(= \frac{5}{16}\)
Kudos Please... If my post helped.
