Suppose you flip 50 fair coins.

(a) How many possible outcomes (microstates) are there?

(b) How many ways are there of getting exactly 25 heads and 25 tails?

(c) What is the probability of getting exactly 25 heads and 25 tails?

(d) What is the probability of getting exactly 30 heads and 20 tails?

(e) What is the probability of getting exactly 40 heads and 10 tails?

(f) What is the probability of getting 50 heads and no tails?

(g) Plot a graph of the probability of getting n heads, as a function of n.

Solution 3P

Now suppose we flip 20 coins.

The number of possible outcomes( microstates) is given by

The number of microstates and probabilities of a few macro states are as follows

no of heads |
no of micro states |
probability |

25 |
1.264 |
0.112 |

30 |
4.713 |
0.042 |

40 |
1.027 |
9.1 |

50 |
1 |
8.8 |

A graph of the probability of getting n heads, as a function of n is as shown below