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When two coins are tossed simultaneously, what are the chances of getting at least one tail?
- a)3/4
- b)1/5
- c)4/5
- d)1/4
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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When two coins are tossed simultaneously, what are the chances of gett...
When two coins are tossed , then possible outcomes are : HH ; HT ; TT ; TH Total possible outcomes =4 The outcomes in which one or more head occurs are : HT ; HH ; TH No. of favorable outcomes =3 required probability = no. of favourable outcomes/ total outcomes = 3/4
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When two coins are tossed simultaneously, what are the chances of gett...
To find the chances of getting at least one tail when two coins are tossed simultaneously, we can use the concept of probability.
Let's consider the possible outcomes when two coins are tossed:
- Outcome 1: Both coins land on heads (HH)
- Outcome 2: One coin lands on heads and the other on tails (HT or TH)
- Outcome 3: Both coins land on tails (TT)
So, we have a total of three possible outcomes, out of which only one outcome does not have at least one tail (HH). The remaining two outcomes have at least one tail.
Therefore, the chances of getting at least one tail can be calculated as the ratio of the favorable outcomes to the total possible outcomes.
Favorable outcomes: 2 (HT and TH)
Total possible outcomes: 3 (HH, HT, and TH)
Probability = Favorable outcomes / Total possible outcomes
= 2/3
Now, we need to simplify this fraction. We can multiply both the numerator and denominator by 1/2 to get a simpler form:
Probability = (2/3) * (1/2)
= 2/6
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Probability = 1/3
So, the chances of getting at least one tail when two coins are tossed simultaneously is 1/3.
However, none of the given options (a, b, c, d) matches the correct answer. Therefore, the correct answer is e) None of these.
Let's consider the possible outcomes when two coins are tossed:
- Outcome 1: Both coins land on heads (HH)
- Outcome 2: One coin lands on heads and the other on tails (HT or TH)
- Outcome 3: Both coins land on tails (TT)
So, we have a total of three possible outcomes, out of which only one outcome does not have at least one tail (HH). The remaining two outcomes have at least one tail.
Therefore, the chances of getting at least one tail can be calculated as the ratio of the favorable outcomes to the total possible outcomes.
Favorable outcomes: 2 (HT and TH)
Total possible outcomes: 3 (HH, HT, and TH)
Probability = Favorable outcomes / Total possible outcomes
= 2/3
Now, we need to simplify this fraction. We can multiply both the numerator and denominator by 1/2 to get a simpler form:
Probability = (2/3) * (1/2)
= 2/6
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Probability = 1/3
So, the chances of getting at least one tail when two coins are tossed simultaneously is 1/3.
However, none of the given options (a, b, c, d) matches the correct answer. Therefore, the correct answer is e) None of these.
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