Question

There are 15 coins in a jar, 8 of them are gold and the others silver. 5 coins are randomly drawn.What is the probability that 2 of the coins drawn are gold and 3 are silver? Enter your answer as adecimal number rounded to TWO digits after the decimal point.

Answer 1

Step 1

Given;

`\begin{gathered} Total\text{ number of coins=15} \\ Total\text{ number of gold=8} \\ Total\text{ number of silver=7} \\ \end{gathered}`

Required; 5 coins are randomly drawn. What is the probability that 2 of the coins drawn are gold and 3 are silver?

Step 2

Where;

`\begin{gathered} P=(8)/(15),\text{ x=2} \\ P(2)=(5!)/(2!(5-2)!)((8)/(15))^2(1-(8)/(15))^(5-2) \\ =0.28907983539095 \\ \approx0.29 \end{gathered}`

Answer;

`0.29\text{ to 2 decimal places}`