Question

A fair coin is tossed 4 times. The probability that heads exceed tails in number is?
$
  A.\dfrac{3}{{16}} \\
  B.\dfrac{1}{4} \\
  C.\dfrac{5}{{16}} \\
  D.\dfrac{7}{{16}} \\
$

Answer 1

Hint: In order to solve this problem we need to know that when a coin is tossed it can give only two outcomes head or tail then we need to find the number of outcomes the coin can give in different arrangement that will be total number of outcomes and the out comes in which the number of heads are more than that of tail that will be our favorable outcomes. Then we need to apply the formula of probability that is number of favorable outcomes upon total number of outcomes. This will give you the right answer.

Complete step by step answer:
We know that a coin can give heads or tails that is 2 outcomes.
If it is tossed n times then it can give ${2^n}$ outcomes.
Here it is being tossed 4 times it means it will give ${2^4} = 16$ outcomes.
So, the total number of outcomes is 16.
We need to get the number of outcomes in which heads exceed tails.
So, the number of arrangements in which heads exceeds tails is,
{(H,H,H,H), (H,H,H,T), (H,H,T,H), (H,T,H,H),(T,H,H,H)}.
So, there must be three heads or four heads when you toss 4 times the coin to get the number of heads more than tails. If there are two heads then the number of heads and tails will be equal and if there are 1 heads then the number of tails will exceed. So, we can see there are 5 outcomes in which the number of heads exceeds the number of tails.
So, the probability is = $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favorable}}\,{\text{outcomes}}\,}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}} = \dfrac{5}{{16}}$ .

So, the correct answer is “Option C”.

Note: In the problems of tossing a coin you need to consider how many times the coin is tossed to get the total number of outcomes that is if it is tossed n times then the total number of outcomes will be ${2^n}$. This is applicable for everything which gives us the number of outcomes 2 in performing the event once. Then the number of favorable outcomes will be calculated with the help of conditions provided on the problem. Doing this will solve your problem and will give you the right answer.