Question

Ajar contains 10 red marbles numbered 1 to 10 and 6 blue marbles numbered 1 to 6. 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 and even-numbered Your answer is:

Answer 1

Answer:

Given that:

A jar contains 10 red marbles numbered 1 to 10 and 6 blue marbles numbered 1 to 6

Red marble =

R1, R2, ....R10

Blue marble =

B, B2, ....BG

Sample space = $\begin{Bmatrix} R_1,R_2,...R_{10},B_1,B_2,....B_{6} \end{Bmatrix}$

Total =16 marble

a)  The marble is red.

$P(Red)=\frac{Red\ marble}{Total\ marbles}$

P(Red) 10 16

$P(Red)=0.625$

b)  The marble is odd-numbered.

$P(odd)=\frac{\begin{Bmatrix} R_1,R_3,R_5,R_7,R_9,B_1,B_3,B_5 \end{Bmatrix}}{16}$$P(odd)=\frac{8}{16}$

$P(odd)=0.5$

c) The marble is red or odd-numbered.

$P(red\ or\ odd)=\frac{\begin{Bmatrix} R_1,...R_{10},B_1,B_3,B_5 \end{Bmatrix}}{16}$$P(red\ or\ odd)=\frac{ 13}{16}$

d) The marble is blue or even-numbered.

$P(blue\ or\ even)=\frac{\begin{Bmatrix} R_2,R_4,R_6,R_8,R_{10},B_1,...,B_6 \end{Bmatrix}}{16}$$P(blue\ or\ even)=\frac{11}{16}$