Question

There are 14 shirts in a wardrobe Le. 3
black, 5 white, 4 blue and 2 red. If three
shirts are picked at random then what is
the probability of getting 1 shirt of white,
blue and red, each?​

Answer 1

Step-by-step explanation:

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Answer 2

: Answer:

The probability of getting 1 shirt of white, blue, and red, is 15/91.

Step-by-step explanation:

Given,

The total number of shirts is 14

The number of black shirts is 3

The number of blue shirts is 4

The number of red shirts is 2

To find,

The probability of getting 1 shirt of white, blue and red, each.

Work to be done,

Three shirts are to be picked at random 1 white, 1 blue, and 1 red.

Calculation,

Let 'E' be the event of picking 3 shirts from 14 shirts.

Let 'A' be the event of picking 1 white shirt.

Let 'B' be the event of picking 1 blue shirt.

Let 'C' be the event of picking 1 red shirt.

Then,

$n(E) = ^{14}C_3,\ n(A) = ^5C1, \ n(B) = ^4C_1, \ n(C) = ^2C_1$

So, the probability of the event 'E' to happen is:

$P(E) = \frac{(n(A) \times n(B) \times n(C)}{n(E)}$

$\implies P(E) = \frac{^5C_1\times ^4C_1 \times ^3C_1}{^{14}C_3}$

⇒ P(E) = (5 × 4 × 3)/364

⇒ P(E) = 15/91

Therefore, the probability of getting 1 shirt of white, blue, and red, is 15/91.

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