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Two unbiased coins are tossed together five times. What is the probability that heads turn up on both the coins for three times?
- a)9/512
- b)27/512
- c)45/512
- d)63/512
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two unbiased coins are tossed together five times. What is the probab...
The probability that heads turn up when two coins are tossed = (1/2)(1/2) = ¼
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∴ The probability that three times heads turn up on both the coins
= 5C3 (1/4)3 (1-1/4)2
= (10) (1/64)(9/16) = 45/512
Most Upvoted Answer
Two unbiased coins are tossed together five times. What is the probab...
To solve this problem, we need to use the concept of probability.
Given that two unbiased coins are tossed together five times, we need to find the probability that heads turn up on both coins three times.
Let's break down the problem into smaller steps:
Step 1: Find the total number of possible outcomes when two coins are tossed together.
When two coins are tossed together, each coin has two possible outcomes - either heads (H) or tails (T). Since there are two coins, the total number of possible outcomes is 2 * 2 = 4.
Step 2: Find the number of favorable outcomes when heads turn up on both coins three times.
Since we want heads to turn up on both coins three times, we need to have three outcomes where both coins show heads (HH) and two outcomes where both coins show tails (TT). The remaining outcomes can be either heads or tails.
To calculate the number of favorable outcomes, we can use the binomial coefficient formula:
C(n, r) = n! / (r! * (n-r)!), where n is the total number of trials and r is the number of successful trials.
In this case, n = 5 (total number of trials) and r = 3 (number of successful trials).
So, the number of favorable outcomes is C(5,3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3 * 2!) / (3 * 2!) = 10.
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 10 / 4 = 5/2 = 5 * 1/2 = 5 * 0.5 = 2.5
However, probability should always be between 0 and 1. Since the calculated probability is greater than 1, it is not possible.
Therefore, the correct answer is None of these.
Given that two unbiased coins are tossed together five times, we need to find the probability that heads turn up on both coins three times.
Let's break down the problem into smaller steps:
Step 1: Find the total number of possible outcomes when two coins are tossed together.
When two coins are tossed together, each coin has two possible outcomes - either heads (H) or tails (T). Since there are two coins, the total number of possible outcomes is 2 * 2 = 4.
Step 2: Find the number of favorable outcomes when heads turn up on both coins three times.
Since we want heads to turn up on both coins three times, we need to have three outcomes where both coins show heads (HH) and two outcomes where both coins show tails (TT). The remaining outcomes can be either heads or tails.
To calculate the number of favorable outcomes, we can use the binomial coefficient formula:
C(n, r) = n! / (r! * (n-r)!), where n is the total number of trials and r is the number of successful trials.
In this case, n = 5 (total number of trials) and r = 3 (number of successful trials).
So, the number of favorable outcomes is C(5,3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3 * 2!) / (3 * 2!) = 10.
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 10 / 4 = 5/2 = 5 * 1/2 = 5 * 0.5 = 2.5
However, probability should always be between 0 and 1. Since the calculated probability is greater than 1, it is not possible.
Therefore, the correct answer is None of these.
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Two unbiased coins are tossed together five times. What is the probability that heads turn up on both the coins for three times?a) 9/512b) 27/512c) 45/512d) 63/512e) None of theseCorrect answer is option 'C'. Can you explain this answer?
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