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Difficulty:
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Question Stats:
57% (03:10) correct
43%
(02:27)
wrong
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Thierry tosses a fair coin twice, and Melvil then tosses it three times. What is the probability that Melvil obtains more heads than Thierry?
A. \(\frac{1}{2}\)
B. \(\frac{9}{16}\)
C. \(\frac{19}{32}\)
D. \(\frac{5}{8}\)
E. \(\frac{3}{4}\)
A. \(\frac{1}{2}\)
B. \(\frac{9}{16}\)
C. \(\frac{19}{32}\)
D. \(\frac{5}{8}\)
E. \(\frac{3}{4}\)
ankushsambare
Joined: 13 Jun 2022
Last visit: 31 Aug 2026
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02 Jul 2026, 08:56
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Let T be the number of heads Thierry gets in 2 tosses, and M be the number of heads Melvil gets in 3 tosses.
Thierry's probabilities:
7/32 + 8/32 + 1/32 = 16/32 = 1/2
Answer: A. 1/2
Thierry's probabilities:
- P(T = 0) = 1/4
- P(T = 1) = 1/2
- P(T = 2) = 1/4
- P(M = 0) = 1/8
- P(M = 1) = 3/8
- P(M = 2) = 3/8
- P(M = 3) = 1/8
- If Thierry gets 0 heads (probability = 1/4), Melvil needs at least 1 head.
- Probability = 7/8
- Contribution = (1/4) × (7/8) = 7/32
- If Thierry gets 1 head (probability = 1/2), Melvil needs at least 2 heads.
- Probability = 3/8 + 1/8 = 1/2
- Contribution = (1/2) × (1/2) = 8/32
- If Thierry gets 2 heads (probability = 1/4), Melvil must get 3 heads.
- Probability = 1/8
- Contribution = (1/4) × (1/8) = 1/32
7/32 + 8/32 + 1/32 = 16/32 = 1/2
Answer: A. 1/2
02 Jul 2026, 09:47
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One nice shortcut is the following: what’s the probability that after two flips Melvil has the same number of heads as Thierry ?
