First find the number of favorable outcomes and the total number of outcomes.
516, or about 31.25 %
Practice makes perfect
We are told that in a game show that airs on television five days per week, a prize is placed behind one of the two doors. Then, the contestant wins the prize by selecting the correct door. We will find the probability that exactly two of the five contestants win a prize during a week. We will first find the number of outcomes in the sample space. Let W represent a win, and L represent a lose.
Now we will find the number of favorable outcomes and the total number of outcomes. From the table we can see that the number of favorable outcomes is 10. We will find the total number of outcomes by adding the number of outcomes of the different number of winners.
1+5+10+10+5+1= 32
The total number of outcomes is 32. From here we will decide the formula that we will use. Since the prizes are randomly placed behind one of the doors, the outcomes should be equally likely. Therefore, we will us the Theoretical Probability Formula. Let's find the desired probability.
P(exactly two winners)=Number of favorable outcomes/Total number of outcomes
