An urn contains 2 red marbles and 3 blue marbles. 1. One person takes two marbles at random from the urn and does not replace th

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An urn contains 2 red marbles and 3 blue marbles. 1. One person takes two marbles at random from the urn and does not replace th

em. a) State the general ways in which the person could get a red marble and a blue marble b) State the number of ways this can occur. c) What is the probability the person gets a red and a blue marble? P(R & B) =

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-03-21T23:01:52+03:00

Answer with explanation:

Let’s consider: An urn is composed of 2 red marbles and 3 blue marbles.

Total number of marbles = 2 + 3 = 5

a) The possible ways for the person to select one red marble and one blue marble include:

1) Drawing a red marble first, followed by a second blue marble.

2) Drawing a blue marble first and then picking a red marble second.

b) The total number of combinations for selecting one red and one blue marble is represented as:-

$^2C_1\times^3C_1=2\times3=6$ (i)

c) The count of ways to draw 2 marbles from 5 is defined as:-

$^5C_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5\times4\times3!}{3!\times2}=10$ (ii)

Now, the probability of the individual selecting a red and a blue marble can be calculated as:-

$P(R\ \&B)=\dfrac{6}{10}=0.6$ [Divide (i) by (ii)]

Consequently, the probability of selecting a red and a blue marble= 0.6