A high school theater club has 40 students, of whom 6 are left-handed. Two students from the club will be selected at random, on

Question

3 months ago

11

e at a time without replacement. What is the probability that the 2 students selected will both be left-handed?

1 answer:

babunello [11.8K] · Answer 1 · 2026-02-28T19:41:26+03:00

Response:

$1.92\%$

Detailed explanation:

Probability for an event is calculated as the ratio of the size of the event space compared to that of the sample space.

The sample space encompasses all possible outcomes.

Event space represents the number of favorable outcomes for the event in question.

Thus

Let

x ------> size of event space

y ----- → size of sample space

so

$P=\frac{x}{y}$

Calculate the probability of the first student being left-handed

we have

$x=6$

$y=40$

substituting values

$P=\frac{6}{40}$

Simplify

$P=\frac{3}{20}$

Calculate the probability of the second student being left-handed

we have

$x=6-1=5$

$y=40-1=39$

substituting values

$P=\frac{5}{39}$

Calculate the probability that both selected students will be left-handed

Multiply the probabilities together.

$P=\frac{3}{20}(\frac{5}{39})=\frac{15}{780}$

Convert to percentage

Multiply by 100

$\frac{15}{780}(100)=1.92\%$