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If 8 coins are tossed, what is the chance that one and only one will turn up Head?
- a)1/16
- b)3/35
- c)3/32
- d)1/32
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If 8 coins are tossed, what is the chance that one and only one will t...
One head and seven tails would have eight positions where the head can come.
Thus, 8 x (1/2)8 = (1/32)
Thus, 8 x (1/2)8 = (1/32)
Most Upvoted Answer
If 8 coins are tossed, what is the chance that one and only one will t...
To determine the chance of getting one and only one head when tossing 8 coins, we can use the concept of combinations.
**Understanding the Problem:**
We have 8 coins, and each coin can either turn up heads or tails. So, for each coin, there are 2 possible outcomes (heads or tails). Therefore, the total number of possible outcomes for all 8 coins is 2^8 = 256.
**Solving the Problem:**
To find the chance of getting one and only one head, we need to determine the number of favorable outcomes (one head) and divide it by the total number of possible outcomes (256).
**Finding the Number of Favorable Outcomes:**
To find the number of favorable outcomes, we can use combinations. Since we need only one head, we can choose one coin out of the eight coins to be heads. This can be done in C(8, 1) = 8 ways.
**Calculating the Probability:**
The probability of an event happening is given by the formula: Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes.
Number of Favorable Outcomes = 8
Total Number of Possible Outcomes = 256
Probability = 8 / 256 = 1 / 32
Therefore, the chance that one and only one coin will turn up heads is 1/32.
Hence, the correct answer is option D) 1/32.
**Understanding the Problem:**
We have 8 coins, and each coin can either turn up heads or tails. So, for each coin, there are 2 possible outcomes (heads or tails). Therefore, the total number of possible outcomes for all 8 coins is 2^8 = 256.
**Solving the Problem:**
To find the chance of getting one and only one head, we need to determine the number of favorable outcomes (one head) and divide it by the total number of possible outcomes (256).
**Finding the Number of Favorable Outcomes:**
To find the number of favorable outcomes, we can use combinations. Since we need only one head, we can choose one coin out of the eight coins to be heads. This can be done in C(8, 1) = 8 ways.
**Calculating the Probability:**
The probability of an event happening is given by the formula: Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes.
Number of Favorable Outcomes = 8
Total Number of Possible Outcomes = 256
Probability = 8 / 256 = 1 / 32
Therefore, the chance that one and only one coin will turn up heads is 1/32.
Hence, the correct answer is option D) 1/32.
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