Question

Suppose four coins are tossed. Let X represents the number of tails that occur. Illustrate a probability distribution of a random variable X using fraction.

Answer 1

Answer:

There are 2^4 possible results, which is 16 possible results. They are split between the following: 4 tails; 3 tails and a head; 2 tails and 2 heads; 3 heads and a tail; and 4 heads.

There is one way and only one way to get 4 tails - where all four coins are tails. In the same way, there is only one way to get 4 heads - where all four coins are heads. This accounts for 2 of the 16 possible results .

There are 4 ways to get to get 3 tails and a head - where the first coin is a head and the other three tails; where the second coin is a head and the other three tails; where the third coin is a head and the other three tails; and where the fourth coin is a head and the other three tails. In the same way there are 4 ways to get three heads and a tail - where the first coin is a tail and the other three heads; etc.

This accounts for 8 of the 16 possible results.

Together the four of a kind and three of one kind and one of the other account for 10 of the 16 possible results.

Since the only other possible combination is two heads and two tails, the total number of possible results of that combination is the difference between the total combinations, 16, and the other combinations computed above - 16 minus 10 is 6 combinations.

Therefore, the probability distribution for x, the number of tails, is as follows:

4 tails = 1/16

3 tails = 4/16

2 tails = 6/16

1 tail = 4/16

0 tails = 1/16

There will be at least 1 tail thrown 15/16 of the time.

I hope this helps.

Answer 2

Answer:

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