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A coin is tossed and a die is rolled. Find the probability of getting heads on the coin and a multiple of 4 on the die.
- a)1/6
- b)1/12
- c)1/3
- d)2/7
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A coin is tossed and a die is rolled. Find the probability of getting ...
Understanding the Problem
To find the probability of two independent events occurring simultaneously (getting heads on a coin toss and rolling a multiple of 4 on a die), we can use the multiplication rule of probability.
Step 1: Probability of Getting Heads on the Coin
- A coin has two sides: heads (H) and tails (T).
- The probability of getting heads (P(H)) is:
Step 2: Probability of Rolling a Multiple of 4 on the Die
- A standard die has six faces: 1, 2, 3, 4, 5, and 6.
- The multiples of 4 on a die are: 4.
- The total number of outcomes when rolling a die is 6.
- The probability of rolling a multiple of 4 (P(Multiple of 4)) is:
Step 3: Calculating the Combined Probability
- Since the coin toss and die roll are independent events, the combined probability (P) is found by multiplying the individual probabilities:
Conclusion
Thus, the probability of getting heads on the coin and a multiple of 4 on the die is:
1/12
Hence, the correct answer is option 'B'.
To find the probability of two independent events occurring simultaneously (getting heads on a coin toss and rolling a multiple of 4 on a die), we can use the multiplication rule of probability.
Step 1: Probability of Getting Heads on the Coin
- A coin has two sides: heads (H) and tails (T).
- The probability of getting heads (P(H)) is:
- P(H) = 1/2
Step 2: Probability of Rolling a Multiple of 4 on the Die
- A standard die has six faces: 1, 2, 3, 4, 5, and 6.
- The multiples of 4 on a die are: 4.
- The total number of outcomes when rolling a die is 6.
- The probability of rolling a multiple of 4 (P(Multiple of 4)) is:
- P(Multiple of 4) = Number of favorable outcomes / Total outcomes
- P(Multiple of 4) = 1/6
Step 3: Calculating the Combined Probability
- Since the coin toss and die roll are independent events, the combined probability (P) is found by multiplying the individual probabilities:
- P = P(H) × P(Multiple of 4)
- P = (1/2) × (1/6) = 1/12
Conclusion
Thus, the probability of getting heads on the coin and a multiple of 4 on the die is:
1/12
Hence, the correct answer is option 'B'.
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Community Answer
A coin is tossed and a die is rolled. Find the probability of getting ...
P(A) = P(heads on the coin) = 1/2
P(B) = P (multiple of 4 on the die) = 1/6
Since events are independent, therefore:
P(A and B) = P(A) x P(B) =
P(B) = P (multiple of 4 on the die) = 1/6
Since events are independent, therefore:
P(A and B) = P(A) x P(B) =
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A coin is tossed and a die is rolled. Find the probability of getting heads on the coin and a multiple of 4 on the die.a)1/6b)1/12c)1/3d)2/7Correct answer is option 'B'. Can you explain this answer?
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