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 $\\frac{1}{2}$.
Important Questions from Probability (Notes)
- A box contains 20 black, 22 white, and 24 red socks. If a person draws socks at random one by one without looking, what is the minimum number of socks she must pick to be certain of having at least one pair of black socks?
The following bus schedule is seen at a bus stop located somewhere in between town A and town B.
Town A-00:10, then every 20 mins
Town B-00:15, then every 20 mins
If a person arrives at this bus stop at some random time, the probability that the next bus is for town B is- Some, but not all, faces of a six-faced cubical fair die are painted red (R) and the remaining green (G); and the die is thrown until red faces come up on top 4 times.
Consider the following sequences of colours listed left to right as they appear on the top.
A: GRRRR
B: GRGRRR
Which one of the following is true? - 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?
