Question

Im not the best at word problems A box of jerseys for a pick-up game of basketball contains 10 extra-large jerseys, 7 large jerseys, and 5 medium jerseys. If you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 medium jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth

Answer 1

Given:

The number of extra-large jerseys is 10.

The number of large jerseys is 7.

The number of medium jerseys is 5.

Three jerseys to be taken.

To find the probability that randomly grabs 3 medium jerseys:

The probability is,

`\begin{gathered} P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \\ =(^5C_3)/(^(22)C_3) \\ =((5!)/((5-3)!3!))/((22!)/((22-3)!3!)) \\ =((5!)/(2!3!))/((22!)/(19!3!)) \\ =(5*4*3)/(22*21*20) \\ =(1)/(154) \end{gathered}`

Hence, the probability that randomly grabs 3 medium jerseys is,

`(1)/(154)`