Question

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?.

Answer 1

The theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

What is theoretical probability?

Theoretical probability of an event is the ratio of number of favourable outcome to the total expected number of outcome of that event.

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.

• The total number of names are 5.
• The total number of names chosen are 4.

The total number of ways 4 names can be taken out from 5 names is,

$^5C_4$.

Here one spot needs to be fixed for Chandra. Now the total number of outcome remain 4 and favourable outcome remain 3.

Thus, the number of ways 4 names can be taken out such that it contains the name Chandra is

$^4C_3$.

The theoretical probability that Chandra will be chosen as one of the science fair participants is,

$P=\dfrac{^4C3}{^5C4}\\P=\dfrac{4}{5}\\P=0.8\\P=80\%$

Thus, the theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

Learn more about the theoretical probability here;

brainly.com/question/8652467

#SPJ1