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Question: A coin is tossed 5 times. The probability of 2 heads and 3 tails is: A. \(\dfrac{{11}}{{16}}\) B...

A coin is tossed 5 times. The probability of 2 heads and 3 tails is:
A. 1116\dfrac{{11}}{{16}}
B. 516\dfrac{5}{{16}}
C. 1132\dfrac{{11}}{{32}}
D. 532\dfrac{5}{{32}}

Explanation

Solution

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 12\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 2n2^n
In question the coin is tossed 5 times then, the total number of outcomes is 25{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 =25=16=2^5=16.

Then, the probability of getting 2 heads and 3 tails is,
P(E)=Favorable outcomesTotalnumber of outcomes P(E)=1025 P(E)=516  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 516\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.