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There are 18 marbles in a bag, all of the same size. The marbles are in the ratio 2:3:4 having the colours red, green and blue respectively.
a)Find the number of each colour of the marbles.
b)If two marbles are selected at random one after the other and replaced, find
i)all are blue.
ii)they are of the same colour.
​

Sagot :

chibabykalu16

Answer:

a)

Red = 4 marbles

Green = 6 marbles

Blue = 8 marbles

b) i)

P(BB) = 16/81

b) ii)

P(they are of the same color) = 116/324

Step-by-step explanation:

Given:

Red : Green: Blue = 2:3:4

a)Find the number of each color of the marbles.

  • Red = 2/9 * 18 = 4 marbles
  • Green = 3/9 * 18 = 6 marbles
  • Blue = 4/9 * 18 = 8 marbles

bi) All are blue

First marble is blue: 8/18 (since there are 8 blue marbles out of 18)

The second marble is blue (replaced): 8/18

The probability of both being blue: The first

P(BB) = 8/18 * 8/18

= 64/324 = 16/81

Note: P(BB) Means the probability of two blue marbles being selected

b ii)

The probability that they are of the same color, which means they may be both red, both green, or both blue

We need to find the probability of each marble color and then add it together

P(RR) = 4/18 * 4/18 = 16/324 = 4/81

P(GG) = 6/18 * 6/18 = 36/324 = 1/9

P(BB) = 8/18 * 8/18 = 64/324 = 16/81 (From b i)

Therefore, P(they are of the same color)

= 16/324 + 36/324 + 64/324

= 116/324

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