Question

There are twenty-one sweets in a box. Out of them, nine are blue and twelve are green in color. Riya picked two sweets at random. What is the probability that both the sweets are chosen are blue in color? (Give your answer as a percent, don't forget the %. Round to the nearest whole number if necessary.)

Answer 1

Given:

The number of blue sweets is 9.

The number of green sweets is 12.

Two sweets are picked at random.

To find:

The probability that both the sweets are chosen is blue in colour.

Step-by-step explanation:

Using the combination rule,

`\begin{gathered} P(Both\text{ blue\rparen= }\frac{Number\text{ }of\text{ }favourable\text{ }outcomes}{Total\text{ n}umber\text{ }of\text{ }outcomes} \\ =(^9C_2)/(^(21)C_2) \\ =((9!)/((9-2)!2!))/((21!)/((21-2)!2!)) \\ =((9!)/(7!2!))/((21!)/(19!2!)) \\ =(8*9)/(20*21) \\ =(72)/(420) \\ =(6)/(35) \end{gathered}`

Convert into a percentage,

`\begin{gathered} (6)/(35)*100\text{ \%}=17.14\text{ \%} \\ \approx17\text{ \%} \end{gathered}`

Final answer:

The probability that both the sweets are chosen is blue in colour in percentage is 17%.