Question

A jar contains 10 red marbles numbered 1 to 10 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability of the given event.

(a) The marble is red
Your answer is :     

(b) The marble is odd-numbered
Your answer is :     

(c) The marble is red or odd-numbered
Your answer is :     

(d) The marble is blue or even-numbered
Your answer is :

Answer 1

Given that, a jar contains 10 red marbles numbered 1 to 10 and 4 blue marbles numbered 1 to 4.

Total number of marbles = 10 + 4 = 14

A marble is drawn at random from the jar of 14 marbles, we want to find, the probablities,

a) P(red marble) = 10/14 = 0.7143

P(the marble is red) = 0.7143

b) There are total 7 even and 7 odd number of marbles,

Therefore, P(odd) = P(even) = 7/14 = 0.5

P(the marble is odd-numbered) = 0.5

c) since, there are 5 marbles are red and odd-numbered,

P(Red and odd) = 5/14

Therefore,

P(red OR odd)

= P(red) + P(odd) - P(red and odd)

= 10/14 + 7/14 - 5/14

= 12/14

= 0.8571

P(the marble is red or odd-numbered) = 0.8571

d) since, there are 2 marbles are blue and even-numbered,

P(blue and even) = 2/14

Therefore,

P(blue OR even)

= P(blue) + P(even) - P(blue and even)

= 4/14 + 7/14 - 2/14

= 9/14

= 0.6429

P(the marble is blue or even-numbered) = 0.6429