The probability of getting a royal flush when you deal out a five card hand is 1.54 × 10^-6. Suppose you deal out 8 × 10^6 hands, what is the probability that you will get 0 royal flushes? Make a list of the probabilities that you will get n royal flushes, for n=1 to n=10.
Answer of Part1)P (Getting a royal flush when you deal out a five card hand) = 1.54 × 10-6
Therefore, P (Getting zero royal flushes when you deal out a 8 × 106 hands)
= 0.99 × 8 × 106
= 0.000004462
Please help me with answer of Part2)
Your answer for 0 royal flushes is correct. For other numbers, use the binomial distribution formula. You can find it described at
(Broken Link Removed) and in most probability textbooks
Thanks drwls
To calculate the probabilities of getting a specific number of royal flushes, we can use the binomial distribution formula. The formula for the probability of getting exactly k successes in n independent trials, each with a probability p of success, is:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
In this case, n = 8 × 10^6 (the number of hands) and p = 1.54 × 10^-6 (the probability of getting a royal flush on a single hand).
To calculate the probabilities for n=1 to n=10, we need to substitute the values of k into the formula and evaluate them.
Here is the list of probabilities for getting n royal flushes, where n ranges from 1 to 10:
P(1) = (8 × 10^6 choose 1) * (1.54 × 10^-6)^1 * (1 - 1.54 × 10^-6)^(8 × 10^6 - 1)
P(2) = (8 × 10^6 choose 2) * (1.54 × 10^-6)^2 * (1 - 1.54 × 10^-6)^(8 × 10^6 - 2)
P(3) = (8 × 10^6 choose 3) * (1.54 × 10^-6)^3 * (1 - 1.54 × 10^-6)^(8 × 10^6 - 3)
...
P(10) = (8 × 10^6 choose 10) * (1.54 × 10^-6)^10 * (1 - 1.54 × 10^-6)^(8 × 10^6 - 10)
To calculate these probabilities, you will need to perform calculations using large numbers. It is recommended to use a calculator or statistical software for these computations.