Question

इस बीच टॉस अ कॉइन 15 टाइम्स बट इंस्पेक्टर आउटक​

Answer 1

Answer:

In an experiment, n coins are tossed, with each one showing up heads with probability p independently of the others. Each of the coins which shows up heads is then tossed again. What is the probability of observing 5 heads in the second round of tosses, if we toss 15 coins in the first round and p = 0.4? (Hint: First find the mass function of the number of heads observed in the second round.)

While solving this question i calculated the all the scenario where i get heads > 5 in first toss and then I solved for 5 heads in first round of toss and then i multiplied it with the probability of getting 5 heads in the second round in each of the scenario eg :

Case 1 : 1st toss (5H,10T) 2nd toss (5H,0T) = 15C5*(0.4^5)*(0.6^10) * 5C0*(0.4^5)(0.6^0)

Case 2 : 1st toss (6H,9T) 2nd toss (5H,1T) = 15C6*(0.4^6)*(0.6^9) * 6C5*(0.4^5)(0.6^1)

Case 3 :1st toss (7H,8T) 2nd toss (5H,2T) = 15C7*(0.4^7)*(.6^8) * 7C5*(0.4^5)(0.6^2)

Similarly i exhausted all the cases till

Case 11 : 1st toss (15H,0T) 2nd toss (5H,10T) = 15C15*(0.4^15)*(.6^0) * 15C5*(.4^5)(.6^10)

then i calculated the mass function as ∑15n=5(15Cn∗nC5∗(0.4n+5∗0.610))