Hello everyone!
This is question 3 from the Given Probability Exercise, Data Analysis Column 3.
Please let me know if my approach to this question is correct.
I went in reverse order. So here, since it’s a coin flip, which has two possibilities (heads and tails), we can solve it by finding the valid cases rather than probability, as each possibility has a probability of ½.
In the question, it’s mentioned that the probability of getting heads exactly 5 times is 7/40. So basically, this is (Cases you get exactly 5 heads/ Total valid cases) = (7/40)
Note: This is just a ratio and not actual values.
So, I calculated the valid cases as:
a. 7H’s = 1 case
b. 6H’s & 1T = 7 cases
c. 5H’s & 2T’s = 21 cases
Note: Here, we already knew that we had 7x cases, which simply means x = 3. Therefore, total valid cases = 40*3 = 120
So, now we need to calculate the number of valid cases until the sum = 120
d. 4H’s & 3T’s = 35 cases
e. 3H’s & 4T’s = 35 cases
f. 2H’s & 5T’s = 21 cases
If we add a + b + c + d + e + f = 120, which means, it at least lands on heads 2 times.
Therefore, K = 2