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A coin is tossed 5 times, what is the probability that exactly 3 heads will occur.
- a)5/16
- b)1/32
- c)5/36
- d)3/32
Correct answer is option 'A'. Can you explain this answer?
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A coin is tossed 5 times, what is the probability that exactly 3 heads...
To find the probability of getting exactly 3 heads in 5 coin tosses, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
**Favorable Outcomes:**
To get exactly 3 heads, we need to determine the number of ways we can arrange 3 heads and 2 tails in 5 tosses. This can be calculated using the binomial coefficient formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of tosses and r is the number of heads.
In this case, n = 5 (total number of tosses) and r = 3 (number of heads).
Using the formula:
5C3 = 5! / (3! * (5-3)!) = 5! / (3! * 2!)
= (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1))
= (5 * 4) / (2 * 1)
= 10
Therefore, there are 10 favorable outcomes.
**Total Outcomes:**
The total number of possible outcomes can be calculated using the formula 2^n, where n is the number of tosses.
In this case, n = 5 (number of tosses).
Therefore, there are 2^5 = 32 total outcomes.
**Probability:**
The probability of getting exactly 3 heads can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Outcomes
= 10 / 32
= 5 / 16
Therefore, the correct answer is option A) 5/16.
**Favorable Outcomes:**
To get exactly 3 heads, we need to determine the number of ways we can arrange 3 heads and 2 tails in 5 tosses. This can be calculated using the binomial coefficient formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of tosses and r is the number of heads.
In this case, n = 5 (total number of tosses) and r = 3 (number of heads).
Using the formula:
5C3 = 5! / (3! * (5-3)!) = 5! / (3! * 2!)
= (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1))
= (5 * 4) / (2 * 1)
= 10
Therefore, there are 10 favorable outcomes.
**Total Outcomes:**
The total number of possible outcomes can be calculated using the formula 2^n, where n is the number of tosses.
In this case, n = 5 (number of tosses).
Therefore, there are 2^5 = 32 total outcomes.
**Probability:**
The probability of getting exactly 3 heads can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Outcomes
= 10 / 32
= 5 / 16
Therefore, the correct answer is option A) 5/16.
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A coin is tossed 5 times, what is the probability that exactly 3 heads will occur.a)5/16b)1/32c)5/36d)3/32Correct answer is option 'A'. Can you explain this answer?
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