Question
Out of 6 unbiased coins, 5 are tossed independently and they all result in heads. If the 6$^\text{th}$ is now independently tossed, the probability of getting head is
The correct answer is
1/2
Probability of Independent Coin Toss
The question asks for the probability of getting a head when the 6th coin is tossed.
- We are given 6 unbiased coins.
- The first 5 coins were tossed independently and resulted in heads.
- The 6th coin is now tossed independently.
Key Principle: For unbiased coins, each toss is an independent event. The outcome of previous tosses (the first 5 coins) has no influence on the outcome of the 6th toss.
Since the 6th coin is unbiased:
- The probability of getting a head ($P(H)$) is equal to the probability of getting a tail ($P(T)$).
- Mathematically, $P(H) = P(T) = \\frac{1}{2}$.
Therefore, the probability of getting a head on the 6th independent toss is $\\frac{1}{2}$.
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Important Questions from Probability (Notes)
- In a class, 40% and 20% students passed in Mathematics and Physics, respectively, and 10% students passed in both subjects. What is the probability of a randomly selected student to have passed in Physics if the student already passed in Mathematics?
- A stick of length L is broken into two pieces at random. What is the average length of the smaller piece?
- Two students are solving the same problem independently. If the probability that the first one solves the problem is $\frac{3}{5}$ and the probability that the second solves the problem is $\frac{4}{5}$, what is the probability that at least one of them solves the problem?
- A fair die was thrown three times and the outcome was repeatedly six. If the die is thrown again what is the probability of getting six?
- 12 balls, 3 each of the colours red, green, blue and yellow are put in a box and mixed. If 3 balls are picked at random, without replacement, the probability that all 3 balls are of the same colour is
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