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SSSSS [86.1K]
3 years ago
6

A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly

Mathematics
1 answer:
shutvik [7]3 years ago
4 0

Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = \frac{1}{4}

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}

P(First\ White) = \dfrac{3}{10}

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = \frac{1}{4}

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