Question

You are presented with 400 coins. 250 of them are fair coins, while the remaining 150 land tails with probability 0.60.
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 tails?
Part c: Consider the following procedure:
1. Select one of the coins randomly.
2. Flip the coin.
3. Record whether the coin lands heads.
4. Replace the coin and throroughly mix the coins.
If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands heads will be less than 40?

Answer 1

Answer:

Given Data

The total number of coins = 400 =

Total number of fair coins = 250 =

Total number of baised coins = 150 =

Probability that a biased coin land tails = 0.60 =

a) Probability that less than half of them are fair coins , when 60 coins are selected at random

=    , where X is the number of fair coins

  

=  

= 0.0176

probability obtained from , cummulative binomial probability table

b) Probability that a randomly selected coin flipped is baised and it land tails

P[flipped coin is fair] P[coin land tailsgiven fair coin ] + P[flipped coin is baised ] P[coin land tails iven biased coin]

= 0.5375

c) Let Y be the number of times the coin lands head

H = coin selected randomly lands head

F = coin selected randomly is a fair coin

= 0.4625

P=0.4625

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