Question

A bag contains 8 b l a c k marbles, 5 w h i t e marbles, and 3 y e l l o w marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a b l a c k marble and then a y e l l o w marble? b. A bag contains 5 r e d marbles, 3 y e l l o w marbles, and 8 w h i t e marbles. If two different marbles are drawn from the bag , what is the probability of drawing first a r e d marble and then a w h i t e marble?

Answer 1

Answer:

(a). $Probability=\frac{3}{32}$

(b). $Probability=\frac{1}{6}$

Step-by-step explanation:

(a).

The number of Black marbles in the bag = 8

Number of White marbles in the bag = 5

Number of Yellow marbles in the bag = 3

Total marbles in the bag = 16

The probability is given by,

$Probability=\frac{Favourable\ outcomes}{Total\ Possibilities}$

So,

Probability of drawing a Black Marble first is,

$Probability=\frac{8}{16}=\frac{1}{2}$

Now replacement is done.

So,

Probability of drawing Yellow Marble second is,

$Probability=\frac{3}{16}$

So,

Probability is given by,

$Probability=\frac{1}{2}\times \frac{3}{16}\\Probability=\frac{3}{32}$

Therefore, the probability is,

$Probability=\frac{3}{32}$

(b).

Number of Red marbles = 5

Number of Yellow marbles = 3

Number of White marbles = 8

Total marbles = 46

Probability of drawing a Red marble first is given by,

$Probability=\frac{5}{16}$

And,

Probability of drawing a White marble second is given by,

$Probability=\frac{8}{15}$

As, there is no replacement.

So,

Probability is given by,

$Probability=\frac{5}{16}\times \frac{8}{15}\\Probability=\frac{1}{6}$

Therefore, the Probability is given by,

$Probability=\frac{1}{6}$