Question

Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. she randomly selects 2 of the pencils from the box without replacement. what is the probability that both pencils will be sharpened?

Answer 1

1/11

Explanation:

Given:

Bonnie has 4 sharpened and 8 unsharpened pencils in her pencil case. she randomly selects 2 of the pencils from the box without replacement.

Question to Answer:

what is the probability that both pencils will be sharpened?

Solve:

Probability is possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.

Thus we known that,

Bonnie has 4 sharpened and 8 unsharpened pencils.

Hence, the total numbers of pencils is 12.

Let, the probability first one is sharpened be P(E₁) and probability second one is sharpened be P(E₂)

Simplify - P(E₁) = 4/12 = 1/3 and P(E₂) = 3/11

Therefore we have;

P(E) = P(E₁)×P(E₂)

P(E) = 1/3 × 3/11

P(E) = 3/33

P(E) = 1/11

As a result, the probability is 1/11 that both pencils will be sharpened.

Kavinsky