3coins are tossed calculate the followin probabilities p(3heads) p(2heads and 1 tail) p(3 tails)
To calculate the probabilities of different outcomes when tossing three coins, we need to understand the basic principles of probability.
The total number of possible outcomes when tossing a single coin is 2, since a coin can either land heads or tails. Similarly, when tossing three coins, the total number of possible outcomes is 2^3 = 8.
Now let's calculate the probabilities you mentioned step by step:
1. The probability of getting 3 heads (p(3 heads)):
There is only one favorable outcome where all three coins land heads (HHH). So the probability of getting 3 heads is 1 out of 8 possible outcomes, which can be written as 1/8.
2. The probability of getting 2 heads and 1 tail (p(2 heads and 1 tail)):
There are three different ways to achieve this outcome: HHT, HTH, THH. So the probability of getting 2 heads and 1 tail is 3 out of 8 possible outcomes, which can be written as 3/8.
3. The probability of getting 3 tails (p(3 tails)):
Similar to the first case, there is only one favorable outcome where all three coins land tails (TTT). So the probability of getting 3 tails is 1 out of 8 possible outcomes, which can be written as 1/8.
Therefore, the probabilities you requested are:
- p(3 heads) = 1/8
- p(2 heads and 1 tail) = 3/8
- p(3 tails) = 1/8