Question
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. 1611
B. 165
C. 3211
D. 325
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 21 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 2n
In question the coin is tossed 5 times then, the total number of outcomes is 25.
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.
Then, the probability of getting 2 heads and 3 tails is,
P(E)=Totalnumber of outcomesFavorable outcomes P(E)=2510 ⇒P(E)=165
Therefore, the probability of getting a yellow bag is 165
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.