Question

GIVE YOUR ANSWERS IN FRACTION.
A box contains 3 red pencils, 2 blue pencils and 4 green pencils.

Raj chooses 2 pencils at random, without replacement.

Calculate the probability that

(a) they are both red

(b) they are both the same colour

(c) exactly one of the two pencils is green.​

Thankyou​

Answer 1

Answer:

(a) Probability of choosing both red pencils =1/12*

(b)  Probability of choosing two pencils of the same colour  = 7/36

(c) Probability of choosing exactly one green pencil = 1/3 + 4/9 = 7/18

Step-by-step explanation:

Total number of pencils = 3 + 2 + 4 = 9

(a) Probability of choosing a red pencil on the first draw = 3/9

Probability of choosing another red pencil on the second draw (without replacement) = 2/8 = 1/4 (since one red pencil has already been chosen)

Probability of choosing both red pencils = (3/9) x (1/4) = 3/36 = 1/12

(b) Probability of choosing two pencils of the same colour = Probability of choosing two red pencils + Probability of choosing two blue pencils + Probability of choosing two green pencils

Probability of choosing two red pencils = 3/9 x 2/8 = 1/12

Probability of choosing two blue pencils = 2/9 x 1/8 = 1/36

Probability of choosing two green pencils = 4/9 x 3/8 = 1/6

Probability of choosing two pencils of the same colour = 1/12 + 1/36 + 1/6 = 7/36

(c) Probability of choosing exactly one green pencil = Probability of choosing one green and one non-green pencil (i.e., red or blue) + Probability of choosing one non-green (i.e., red or blue) and one green pencil

Probability of choosing one green and one non-green pencil = (4/9) x (6/8) x 2 = 12/36 = 1/3 (since there are two ways to choose one green and one non-green pencil)

Probability of choosing one non-green and one green pencil = (6/9) x (4/8) x 2 = 4/9

Probability of choosing exactly one green pencil = 1/3 + 4/9 = 7/18*

To know more about probability refer:

https://brainly.in/question/20798570

https://brainly.in/question/54143022

#SPJ1