Question

A jar contains 12 red marbles numbered 1 to 12 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 : 3/4 preview (b) the marble is odd-numbered your answer is : 1/2 preview (c) the marble is red or odd-numbered your answer is : 7/8 preview (d) the marble is blue and even-numbered your answer is : 5/8

Answer 1

a) P(getting red)= total number of red marbles possible/all marbles
P(red)=12/(12+4)
P(red)=12/16
P(red)=3/4

b) Between 1-12, 6 possible odd values. Between 1-4, 2 possible odd values
P(odd number) =(6+2)/16
P(odd number)=8/16
P(odd number)=1/2

c) Find probability of getting red OR getting odd number (when 'OR' is used, you add the probabilities)
P(odd or red)=(8/16)+(12/16)
P(odd or red)=20/16 or 1.25 possibility of occurring

d) Probability of getting blue OR getting even number;

P(Blue)=1-(12/16)
P(Blue)=(16/16)-(12/16)
P(Blue)=4/16
P(Blue)=1/4

P(even)=1-(1/2)
P(even)=1/2

Add them together;

P(odd or blue)=(1/4)+(1/2)
P(odd or blue)=(1/4)+(2/4)
P(odd or blue)=3/4

Hope I helped :)

Answer 2

A jar contains 12 red marbles numbered 1 to 12

And 4 blue marbles numbered 1 to 4.

Total number of marbles = 12+4 =16

(a) A marble is drawn at random from the jar. The probability that the marble is red will be =
`(12)/(16)=(3)/(4)`

(b) In all, the odd number marbles are: 1,3,5,7,9,11 (in red) and 1,3(in blue) so total odd number marbles are = 8

So, probability that the marble is odd-numbered is :
`(8)/(16)=(1)/(2)`

(c) The probability that the marble is red or odd-numbered your answer is :

`(12)/(16)+(8)/(16)-(6)/(16)=(14)/(16)=(7)/(8)`

(d) The probability that the marble is blue and even-numbered =

`(4)/(16)+(8)/(16)-(2)/(16)=(10)/(16)=(5)/(8)`