Question

Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?

Answer 1

The probability that a 4 is drawn from A followed by a 2 from B is 1/24

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let us tackle the problem.

Urn A has balls numbered 1 through 6 → Total = 6 balls

The probability of choosing a 4 ( 1 ball ) from Urn A is:

$P(A) = \boxed{\frac{1}{6}}$

Urn B has balls numbered 1 through 4 → Total = 4 balls

The probability of choosing a 2 ( 1 ball ) from Urn B is:

$P(B) = \boxed {\frac{1}{4}}$

The probability that a 4 is drawn from A followed by a 2 from B is

$P(A \cap B) = P(A) \times P(B)$

$P(A \cap B) = \frac{1}{6} \times \frac{1}{4}$

$P(A \cap B) = \boxed {\frac{1}{24}}$

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

Answer 2

Drawing the tree diagram of the problem, we see that there are 6 branches for drawing from Urn A, and then 4 branches for each of the 6 branches, for drawing from Urn B.

This means that there are 6*4=24 possible outcomes, which could be listed as
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1)... (6, 3), (6, 4)},

where the first coordinates represent drawing from urn A, and the second coordinates, drawing from urn B.

(4, 2) is one of these 24, so the probability is 1/24


remark, this problem could also have been solved by the multiplication principle of the probabilities of separate events, that is 1/6 (probability of drawing 4 from Urn A) times 1/4 (probability of drawing 2 from B) = 1/24


Answer: 1/24