Question

A coin is tossed 5 times. The probability of 2 heads and 3 tails is:
A. $\dfrac{{11}}{{16}}$
B. $\dfrac{5}{{16}}$
C. $\dfrac{{11}}{{32}}$
D. $\dfrac{5}{{32}}$

Answer 1

Hint:For a random event, the probability of an event, say p(E) is defined as the ratio of a number of favorable outcomes or chances and the total number of outcomes.Using this definition we try to solve the problem.

Complete step-by-step answer:
When a coin is tossed one time, the probability of getting head or tail is $\dfrac{1}{2}$ i.e number of outcomes will be head or tail i.e. 2 outcomes
If coin is tossed n times then the total outcomes will be $2^n$
In question the coin is tossed 5 times then, the total number of outcomes is ${2^5}$.
Favorable number of outcome is 10, as The favorable number of outcomes of getting 2 heads and 3 tails is 10, i.e. {HHTTT, HTHTT, HTTHT, HTTTH, THTTH, THTHT, THTTH, TTHTH, TTTHH, HTHTT}.

For a random event, the probability of an event, say P(E) is defined as the ratio of a number of favorable outcomes or chances and the total number of outcomes.
Favorable outcomes=10 and Total number of outcomes $=2^5=16$.

Then, the probability of getting 2 heads and 3 tails is,
$
   P(E) = \dfrac{\text{Favorable outcomes}}{\text{Totalnumber of outcomes}} \\
   P(E) = \dfrac{{10}}{{{2^5}}} \\
   \Rightarrow P(E) = \dfrac{5}{{16}} \\
 $
Therefore, the probability of getting a yellow bag is $\dfrac{5}{{16}}$

So, the correct answer is “Option B”.

Note:Basic features of probability-
1. The probability ranges from 0 to 1.
2. The probability of the sum of all events is 1.
3. The probability of a certain event is 1.
4. The probability of an impossible event is 0.