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A man has 5 coins, two of which are double - headed, one is double - tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is
- a)1/5
- b)2/5
- c)3/5
- d)4/5
Correct answer is option 'C'. Can you explain this answer?
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A man has 5 coins, two of which are double - headed, one is double - t...
Required probability = P(DH | H) + P(DT | H)
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A man has 5 coins, two of which are double - headed, one is double - t...
Probability of selecting a coin:
There are a total of 5 coins, so the probability of selecting any one of them is 1/5.
Possible outcomes of the coin toss:
When the selected coin is tossed, there are three possible outcomes: head, tail, or edge.
Calculating the probability of getting a head:
To calculate the probability of getting a head, we need to consider the different types of coins and their probabilities of showing a head.
1. Double-headed coins:
There are two double-headed coins, so the probability of selecting one of them is 2/5. Since both sides of these coins are heads, the probability of getting a head is 1.
2. Double-tailed coin:
There is one double-tailed coin, so the probability of selecting it is 1/5. Since both sides of this coin are tails, the probability of getting a head is 0.
3. Normal coins:
There are two normal coins, so the probability of selecting one of them is 2/5. Since these coins have one head and one tail, the probability of getting a head is 1/2.
Calculating the overall probability:
Now, we can calculate the overall probability of getting a head by considering the probabilities of each type of coin and their respective probabilities of showing a head.
Probability of getting a head = (Probability of selecting a double-headed coin * Probability of getting a head with a double-headed coin) + (Probability of selecting a double-tailed coin * Probability of getting a head with a double-tailed coin) + (Probability of selecting a normal coin * Probability of getting a head with a normal coin)
Probability of getting a head = (2/5 * 1) + (1/5 * 0) + (2/5 * 1/2) = 2/5 + 0 + 1/5 = 3/5
Therefore, the probability that the lower face of the coin is a head is 3/5, which corresponds to option 'C'.
There are a total of 5 coins, so the probability of selecting any one of them is 1/5.
Possible outcomes of the coin toss:
When the selected coin is tossed, there are three possible outcomes: head, tail, or edge.
Calculating the probability of getting a head:
To calculate the probability of getting a head, we need to consider the different types of coins and their probabilities of showing a head.
1. Double-headed coins:
There are two double-headed coins, so the probability of selecting one of them is 2/5. Since both sides of these coins are heads, the probability of getting a head is 1.
2. Double-tailed coin:
There is one double-tailed coin, so the probability of selecting it is 1/5. Since both sides of this coin are tails, the probability of getting a head is 0.
3. Normal coins:
There are two normal coins, so the probability of selecting one of them is 2/5. Since these coins have one head and one tail, the probability of getting a head is 1/2.
Calculating the overall probability:
Now, we can calculate the overall probability of getting a head by considering the probabilities of each type of coin and their respective probabilities of showing a head.
Probability of getting a head = (Probability of selecting a double-headed coin * Probability of getting a head with a double-headed coin) + (Probability of selecting a double-tailed coin * Probability of getting a head with a double-tailed coin) + (Probability of selecting a normal coin * Probability of getting a head with a normal coin)
Probability of getting a head = (2/5 * 1) + (1/5 * 0) + (2/5 * 1/2) = 2/5 + 0 + 1/5 = 3/5
Therefore, the probability that the lower face of the coin is a head is 3/5, which corresponds to option 'C'.
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A man has 5 coins, two of which are double - headed, one is double - tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head isa)1/5b)2/5c)3/5d)4/5Correct answer is option 'C'. Can you explain this answer?
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