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)
- In a box there are 4 white balls and 6 black balls. A ball is drawn at random. If it is white, it is put back along with two more white balls in the box. If it is black, it is put back in the box and then two black balls are thrown out of the box. Now a ball is drawn again at random from the box. Then, what is the probability that it is black?
- A fair coin is tossed three times. Let A be the event of getting exactly two heads and B be the event of getting at most
two tails, then P(A$\cup$B) is: Bag A contains 3 Red and 4 Black balls while Bag B contains 5 Red and 6 Black balls. One ball is drawn at random from one of the bags and is found to be red. Then, the probability that it was drawn from Bag B is
- If we twice flip a balanced coin, what is the probability of getting at least one head?
1. 1/4
2. 2/4
3. 1/6
4. 3/4 Suppose that the random variable X takes on the values: -1, 0, and 2 with probability $\frac{1}{8}$, $\frac{1}{2}$ and $\frac{3}{8}$. Find the expected value of X.
