To determine the expected number of winners in a competition where the probability of winning is 20%, and 90 people participate, you can follow these steps:
1. Understand the Probability:
The probability of winning a prize is given as 20%. This can be written as a decimal for ease of calculation: [tex]\( 20\% = 0.2 \)[/tex].
2. Determine the Total Number of Participants:
Here, we know that there are 90 people entering the competition.
3. Calculate the Expected Number of Winners:
The expected number of winners can be found by multiplying the probability of winning by the total number of participants.
[tex]\[
\text{Expected number of winners} = \text{Probability of winning} \times \text{Number of participants}
\][/tex]
So, we have:
[tex]\[
\text{Expected number of winners} = 0.2 \times 90
\][/tex]
4. Compute the Result:
By performing the multiplication:
[tex]\[
0.2 \times 90 = 18
\][/tex]
Thus, based on the probability and the number of participants, you would expect [tex]\( \boxed{18} \)[/tex] people to win a prize in the competition.
