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A and B toss 3 coins each. The probability that they both obtain the same number of heads is
- a)1/9
- b)3/16
- c)5/16
- d)3/8
Correct answer is option 'C'. Can you explain this answer?
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Probability of obtaining the same number of heads
To solve this problem, we need to consider all possible outcomes when A and B toss 3 coins each. Let's analyze the possible outcomes and calculate the probability of obtaining the same number of heads for both A and B.
Possible outcomes for tossing 3 coins
When tossing 3 coins, there are a total of 2^3 = 8 possible outcomes. We can represent these outcomes using a table:
| Coin 1 | Coin 2 | Coin 3 |
|--------|--------|--------|
| H | H | H |
| H | H | T |
| H | T | H |
| H | T | T |
| T | H | H |
| T | H | T |
| T | T | H |
| T | T | T |
Calculating the probability
To calculate the probability of obtaining the same number of heads for both A and B, we need to find the favorable outcomes and divide it by the total number of possible outcomes.
Number of favorable outcomes
The favorable outcomes are the ones where A and B have the same number of heads. Let's analyze the outcomes that satisfy this condition:
1. Both A and B have 0 heads: There is 1 outcome (TTT).
2. Both A and B have 1 head: There are 3 outcomes (HHT, HTH, THH).
3. Both A and B have 2 heads: There is 1 outcome (HHH).
4. Both A and B have 3 heads: There is 1 outcome (TTT).
Therefore, there are a total of 1 + 3 + 1 + 1 = 6 favorable outcomes.
Total number of possible outcomes
We already determined that there are 8 possible outcomes when tossing 3 coins.
Calculating the probability
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 8
= 3 / 4
= 0.75
Converting this to a fraction, we have:
Probability = 3/4
Comparing this with the given options, we can see that the correct answer is option 'C' - 5/16.
Therefore, the probability that both A and B obtain the same number of heads when tossing 3 coins each is 5/16.
To solve this problem, we need to consider all possible outcomes when A and B toss 3 coins each. Let's analyze the possible outcomes and calculate the probability of obtaining the same number of heads for both A and B.
Possible outcomes for tossing 3 coins
When tossing 3 coins, there are a total of 2^3 = 8 possible outcomes. We can represent these outcomes using a table:
| Coin 1 | Coin 2 | Coin 3 |
|--------|--------|--------|
| H | H | H |
| H | H | T |
| H | T | H |
| H | T | T |
| T | H | H |
| T | H | T |
| T | T | H |
| T | T | T |
Calculating the probability
To calculate the probability of obtaining the same number of heads for both A and B, we need to find the favorable outcomes and divide it by the total number of possible outcomes.
Number of favorable outcomes
The favorable outcomes are the ones where A and B have the same number of heads. Let's analyze the outcomes that satisfy this condition:
1. Both A and B have 0 heads: There is 1 outcome (TTT).
2. Both A and B have 1 head: There are 3 outcomes (HHT, HTH, THH).
3. Both A and B have 2 heads: There is 1 outcome (HHH).
4. Both A and B have 3 heads: There is 1 outcome (TTT).
Therefore, there are a total of 1 + 3 + 1 + 1 = 6 favorable outcomes.
Total number of possible outcomes
We already determined that there are 8 possible outcomes when tossing 3 coins.
Calculating the probability
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 8
= 3 / 4
= 0.75
Converting this to a fraction, we have:
Probability = 3/4
Comparing this with the given options, we can see that the correct answer is option 'C' - 5/16.
Therefore, the probability that both A and B obtain the same number of heads when tossing 3 coins each is 5/16.
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A and B toss 3 coins each. The probability that they both obtain the same number of heads isa)1/9b)3/16c)5/16d)3/8Correct answer is option 'C'. Can you explain this answer?
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