Question

You are presented with 400 coins. 250 of them are fair coins, while the remaining 150 land heads with probability 0.65.

Part a: If you select 60 of the coins at random, what is the probability that less than half of them are fair coins?

Part b: What is the probability that a randomly selected coin flipped once will land heads?

Part c: Consider the following procedure:

1. Select one of the coins randomly.

2. Flip the coin.

3. Record whether the coin lands tails.

4. Replace the coin and thoroughly mix the coins.

If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 40?

Answer 1

Ans: We have total 400 coins out of which saly coins - 250 Untary coins = 150 having bead prob = = 0.65 P (fan coins) Zair coins Total cons 250 =-0.625 kilimo 1.400 ay If we select to coins et random. n = 60 p = pe PCBuy coins) - 0.625 :: P(less than half of then aye Barn coins) - P(X530) · P(x<30). X-nP e 3o-nP Inpa des habide becod Ewe use binomial to norme approximation) °C Z < 30 – 6040065 no 60*0.65 * 0.15 P(2<_-4 113.63 P (2-ne Imp - * -9:4959) 0.0073 Probability that less than halla_0% them are fair is 0.0073 Tag by Probability that candomly selected coin land beads plunga som topfunbar/ - P(fany coin) *P(head/feren)+'p[unfuny coinapp headlaste 250 400 & 0.5 + 150 & 0.65 400 0.3125 + 0.24 375 -0.55 625 6. Probability that randomly selected con land head is 0.55625

Page No.: Date:___ c> Probability that the number of times that the on lands tails will be less than 40. i3 procedure repeated los lime m= 100 P= Prob. that oandomly selected coin Lands Fails - 0:44375 P ( X 240) - 40 mp Inpa P(Z < 40-100% 0:44375 - 100*0.44375 40.35623 P ( x - 4 3 P(Z < =4.975 Plzs - 24.6836 0.88 0 1894 Probability that number of times that the corn land fails will be less than 40 is 0.1894

Ans: We have total 400 coins out of which saly coins - 250 Untary coins = 150 having bead prob = = 0.65 P (fan coins) Zair coins Total cons 250 =-0.625 kilimo 1.400 ay If we select to coins et random. n = 60 p = pe PCBuy coins) - 0.625 :: P(less than half of then aye Barn coins) - P(X530) · P(x<30). X-nP e 3o-nP Inpa des habide becod Ewe use binomial to norme approximation) °C Z < 30 – 6040065 no 60*0.65 * 0.15 P(2<_-4 113.63 P (2-ne Imp - * -9:4959) 0.0073 Probability that less than halla_0% them are fair is 0.0073 Tag by Probability that candomly selected coin land beads plunga som topfunbar/ - P(fany coin) *P(head/feren)+'p[unfuny coinapp headlaste 250 400 & 0.5 + 150 & 0.65 400 0.3125 + 0.24 375 -0.55 625 6. Probability that randomly selected con land head is 0.55625