Simulation of a coin flipping problem Consider the following

Simulation of a coin flipping problem: Consider the following coin flipping problem: For a single flip of an unfair coin, the likelihood of a head is 60% and a tail is 40% The unfair coin is flipped 5 times and number of \'heads\" outcomes is noted. It is desired to find the probability of \"3 heads out of 5 flips\", i.c. P(3 heads out of 5 flips) = ? Show that the theoretical probability of \"3 heads out of 5 flips\" where P(head) = 0.60 is P(3 heads out of 5 flips) = 0.3456 Simulate the problem: simulate the 5 flips and determine if 3 heads resulted run part i) above 1,000 times and find how many times \"3 heads out of 5 flips\"

Solution

X is binomial with p = prob for one head in a toss = 0.6

No of trials = 5

a) Prob (3 heads out of 5 ) = P(X=3)

= 5C3 (0.6)³(0.4)²

= 0.3456

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ii) Expected no of heads in 1000 tosses = np = 1000(0.6) = 600