Question

Consider the toss of four coins. There are 16 (i.e., 24) possible outcomesin one toss. (a)Calculate the probabilities that there is a total number of (1) zero head, (2) one head, (3) two heads, (4) three heads, and (5) four heads appearing on the four coins, respectively.

Answer 1

See answers below

Explanation:

If 4 coins are tossed. the total possible outcomes are;

H H H H , H H H T, H H T H, H T H H, T H H H , H H T T, H T T H, T T H H, H T H T, T H T H, T H H T , H T T T, T H T T, T T H T, T T T H and T T T T

Total outcomes = 16

1) zero head = T T T T = 1 outcome

Probability = Expected/Total outcome

Pr(zero head) = 1/16

2) one head = H T T T, T H T T, T T H T, T T T H = 4 outcomes

Probability = Expected/Total outcome

Probability = 4/16

Pr(one head) = 1/4

3) two heads = H H T T, H T T H, T T H H, H T H T, T H T H, T H H T = 6 outcomes

Probability = Expected/Total outcome

Pr(two head) = 6/16

Pr(two head) = 3/8

4) three heads = H H H T, H H T H, H T H H, T H H H = 4 outcomes

Probability = Expected/Total outcome

Pr(three heads) = 4/16

Pr(two head) = 1/4

5) four heads appearing on the four coins = H H H H = 1 outcome

Pr(four heads) = 1/16