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A and B toss 3 coins. The probability that they both obtain the same number of heads is
- a)51/16
- b)3/16
- c)3/8
- d)1/9
Correct answer is option 'A'. Can you explain this answer?
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A and B toss 3 coins. The probability that they both obtain the same n...
Solution:
When A and B toss 3 coins, the possible outcomes are {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. There are a total of 8 possible outcomes.
Let's consider the cases where A and B obtain the same number of heads:
Case 1: Both obtain 0 heads
There is only one possible outcome: TTT. The probability of this occurring is (1/2)^3 = 1/8.
Case 2: Both obtain 1 head
There are three possible outcomes: HHT, HTH, and THH. The probability of one of these occurring is 3*(1/2)^3 = 3/8.
Case 3: Both obtain 2 heads
There is only one possible outcome: HTT or THT. The probability of this occurring is 2*(1/2)^3 = 1/4.
Case 4: Both obtain 3 heads
There is only one possible outcome: HHH. The probability of this occurring is (1/2)^3 = 1/8.
The probability that A and B obtain the same number of heads is the sum of the probabilities of the cases where they both obtain 0, 1, 2, or 3 heads.
Probability = (1/8) + (3/8) + (1/4) + (1/8) = 51/16
Therefore, the correct answer is option A.
When A and B toss 3 coins, the possible outcomes are {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. There are a total of 8 possible outcomes.
Let's consider the cases where A and B obtain the same number of heads:
Case 1: Both obtain 0 heads
There is only one possible outcome: TTT. The probability of this occurring is (1/2)^3 = 1/8.
Case 2: Both obtain 1 head
There are three possible outcomes: HHT, HTH, and THH. The probability of one of these occurring is 3*(1/2)^3 = 3/8.
Case 3: Both obtain 2 heads
There is only one possible outcome: HTT or THT. The probability of this occurring is 2*(1/2)^3 = 1/4.
Case 4: Both obtain 3 heads
There is only one possible outcome: HHH. The probability of this occurring is (1/2)^3 = 1/8.
The probability that A and B obtain the same number of heads is the sum of the probabilities of the cases where they both obtain 0, 1, 2, or 3 heads.
Probability = (1/8) + (3/8) + (1/4) + (1/8) = 51/16
Therefore, the correct answer is option A.
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A and B toss 3 coins. The probability that they both obtain the same number of heads isa)51/16b)3/16c)3/8d)1/9Correct answer is option 'A'. Can you explain this answer?
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