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An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is
- a)1/9
- b)1/8
- c)2/3
- d)3/8
Correct answer is option 'D'. Can you explain this answer?
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An unbiased coin is tossed three times. The probability that the head ...
Problem:
An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is:
a) 1/9
b) 1/8
c) 2/3
d) 3/8
Solution:
To solve this problem, we need to calculate the probability of getting exactly two heads when tossing an unbiased coin three times. Let's break down the problem into smaller steps:
Step 1: Calculate the total number of possible outcomes:
When tossing a coin three times, each toss has two possible outcomes - either a head or a tail. Since there are three tosses, the total number of possible outcomes is 2 * 2 * 2 = 8.
Step 2: Calculate the number of favorable outcomes:
To find the number of favorable outcomes, we need to determine in how many ways we can get exactly two heads. There are three possible scenarios:
1. Head-Head-Tail (HHT)
2. Head-Tail-Head (HTH)
3. Tail-Head-Head (THH)
So, the number of favorable outcomes is 3.
Step 3: Calculate the probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability of getting exactly two heads is:
P = (Number of favorable outcomes) / (Total number of possible outcomes)
= 3 / 8
Thus, the correct answer is option 'd' - 3/8.
An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is:
a) 1/9
b) 1/8
c) 2/3
d) 3/8
Solution:
To solve this problem, we need to calculate the probability of getting exactly two heads when tossing an unbiased coin three times. Let's break down the problem into smaller steps:
Step 1: Calculate the total number of possible outcomes:
When tossing a coin three times, each toss has two possible outcomes - either a head or a tail. Since there are three tosses, the total number of possible outcomes is 2 * 2 * 2 = 8.
Step 2: Calculate the number of favorable outcomes:
To find the number of favorable outcomes, we need to determine in how many ways we can get exactly two heads. There are three possible scenarios:
1. Head-Head-Tail (HHT)
2. Head-Tail-Head (HTH)
3. Tail-Head-Head (THH)
So, the number of favorable outcomes is 3.
Step 3: Calculate the probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability of getting exactly two heads is:
P = (Number of favorable outcomes) / (Total number of possible outcomes)
= 3 / 8
Thus, the correct answer is option 'd' - 3/8.
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An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases isa)1/9b)1/8c)2/3d)3/8Correct answer is option 'D'. Can you explain this answer?
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