five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the…

five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the regional science fair. their names are placed in a hat, and four names are chosen at random to decide who attends the fair. what is the theoretical probability that chandra will be chosen as one of the science fair participants?\no 25%\no 60%\no 75%\no 80%

five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the regional science fair. their names are placed in a hat, and four names are chosen at random to decide who attends the fair. what is the theoretical probability that chandra will be chosen as one of the science fair participants?\no 25%\no 60%\no 75%\no 80%

Answer

Explanation:

Step1: Identify total and favorable outcomes

Total students are 5, and 4 are to be chosen. Favorable outcome is Chandra being chosen.

Step2: Calculate probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The number of favorable outcomes (Chandra being chosen) is equivalent to the number of ways to choose 3 other students out of the remaining 4 (since Chandra is already in the group), and the total number of ways to choose 4 students out of 5. Using the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, the total number of ways to choose 4 students out of 5 is $C(5,4)=\frac{5!}{4!(5 - 4)!}=5$. The number of ways that Chandra is chosen is equivalent to choosing 3 students out of the remaining 4, $C(4,3)=\frac{4!}{3!(4 - 3)!}=4$. So the probability $P=\frac{4}{5}=0.8$.

Answer:

80%