Question

What is the most probable number of successes in $10$ trials with probability of success ${\displaystyle \frac{2}{3}}$?
A.10
B.7
C.5
D.4

Answer 1

Hint: In this type of question, first explain the given probability, then relate it with another example. At last find the answer by using a probability formula.

Complete step-by-step answer:
To solve this question, first explain the given probability of success.
 Probability of success=${\displaystyle \frac{2}{3}}$
It means out of three trials, $2$ are a success.
We also can consider that out of $9$ trials $6$ are success.
So, the probable number of success in $10$ trials is.
We can find it by using probabilities formula
Most probable number of success in $10$ trials$={\displaystyle \frac{2}{3}}\times 10=6.67$
Which is almost equal to $7$.
Therefore option B is the correct option.

Additional information:
Probability- Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about probabilities.

Note: In these types of questions, we can also use the formula of probability that is favorable outcomes/total number of outcomes. Just calculate the favorable outcomes from the given question and divide it by the total possible outcomes to get the desired results