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There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?
- a)4/9
- b)2/9
- c)1/9
- d)5/9
Correct answer is option 'A'. Can you explain this answer?
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There are three coins. One is a two headed coin (having head on both f...
Let
E1 , E2 and E3 and are events of selection of a two headed coin , biased coin and unbiased coin respectively.
E1 , E2 and E3 and are events of selection of a two headed coin , biased coin and unbiased coin respectively.
Let A = event of getting head. 
Most Upvoted Answer
There are three coins. One is a two headed coin (having head on both f...
Problem Analysis:
- We have three coins: two headed, biased, and unbiased.
- One of the three coins is chosen at random.
- The chosen coin is tossed and it shows heads.
- We need to find the probability that the chosen coin is the two headed coin.
Solution:
Let's calculate the probability step by step.
Step 1: Determine the probability of choosing each coin
- There are three coins, so the probability of choosing each coin is 1/3.
Step 2: Determine the probability of getting heads for each coin
For the two headed coin:
- Since both sides of the coin are heads, the probability of getting heads is 1.
For the biased coin:
- The probability of getting heads is 75%, which can be written as 0.75.
For the unbiased coin:
- The probability of getting heads is 50%, which can be written as 0.5.
Step 3: Calculate the probability of getting heads overall
To calculate the overall probability of getting heads, we need to consider the probability of each coin being chosen and the probability of getting heads for each coin.
Let's assume the event E1 as choosing the two headed coin, E2 as choosing the biased coin, and E3 as choosing the unbiased coin.
Using Bayes' theorem, we can calculate the probability of each event given that heads are obtained:
P(E1|H) = (P(H|E1) * P(E1)) / (P(H|E1) * P(E1) + P(H|E2) * P(E2) + P(H|E3) * P(E3))
= (1 * 1/3) / (1 * 1/3 + 0.75 * 1/3 + 0.5 * 1/3)
= 1 / (1 + 0.75 + 0.5)
= 1 / 2.25
= 4/9
Step 4: Final Answer
The probability that the chosen coin is the two headed coin, given that heads are obtained, is 4/9.
Therefore, the correct answer is option A) 4/9.
- We have three coins: two headed, biased, and unbiased.
- One of the three coins is chosen at random.
- The chosen coin is tossed and it shows heads.
- We need to find the probability that the chosen coin is the two headed coin.
Solution:
Let's calculate the probability step by step.
Step 1: Determine the probability of choosing each coin
- There are three coins, so the probability of choosing each coin is 1/3.
Step 2: Determine the probability of getting heads for each coin
For the two headed coin:
- Since both sides of the coin are heads, the probability of getting heads is 1.
For the biased coin:
- The probability of getting heads is 75%, which can be written as 0.75.
For the unbiased coin:
- The probability of getting heads is 50%, which can be written as 0.5.
Step 3: Calculate the probability of getting heads overall
To calculate the overall probability of getting heads, we need to consider the probability of each coin being chosen and the probability of getting heads for each coin.
Let's assume the event E1 as choosing the two headed coin, E2 as choosing the biased coin, and E3 as choosing the unbiased coin.
Using Bayes' theorem, we can calculate the probability of each event given that heads are obtained:
P(E1|H) = (P(H|E1) * P(E1)) / (P(H|E1) * P(E1) + P(H|E2) * P(E2) + P(H|E3) * P(E3))
= (1 * 1/3) / (1 * 1/3 + 0.75 * 1/3 + 0.5 * 1/3)
= 1 / (1 + 0.75 + 0.5)
= 1 / 2.25
= 4/9
Step 4: Final Answer
The probability that the chosen coin is the two headed coin, given that heads are obtained, is 4/9.
Therefore, the correct answer is option A) 4/9.
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There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?a)4/9b)2/9c)1/9d)5/9Correct answer is option 'A'. Can you explain this answer?
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Solutions for There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?a)4/9b)2/9c)1/9d)5/9Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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