Question

5. A coin is bent so that the probability that it lands heads up is 213. The coin is tossed ten times. Find the probability that it lands heads up at most five times. Find the probability that it lands heads up more times than it lands tails up.

Answer 1

Solution data Given n=10 q=1-P 2=1-3 q=1/5 (9) To find the porobability that it lands heads up at most five times 1. We know that The famula of Binomial distribution is given by P(x) = ne, pa q n-x - P(x) = P x (2) ² (4) That is to find p(xss) P(x<5) = P(x=o) +P (x=1) +P(x-2) + P(x=3)+ P(x=4) + P(*=5) P(xss) =“. (?)*(*)** + 10., (?) () * +, (3) * (3* ? + (3)°43) *097" (43)* (*)** "(3) 6)** 04 P(X55) = 0.00002 +0.00034 + 0.00305 +0.01625 +0.05688+ 0.13653 P(X55) = 0.2131 Therefore the porobability that it tands heads up at most five times is 0.21310

(b) To find the probability that it lands heads up more ♡ times than it lands tails Up The required porobability =P(x>6) = 1-P (x55) = 1-0.2131 = 0.7869 Therefore the probability that it lands heads up more times than it lands tails up is 0.7869 .