Balls

The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?

Correct answer:

p =  0.4196

Step-by-step explanation:

$$\begin{gathered} C_4(14)=\left({\displaystyle \genfrac{}{}{0px}{}{14}{4}}\right)={\displaystyle \frac{14!}{4!(14-4)!}}={\displaystyle \frac{14\cdot 13\cdot 12\cdot 11}{4\cdot 3\cdot 2\cdot 1}}=1001 \\ {C}_2(8)=\left({\displaystyle \genfrac{}{}{0px}{}{8}{2}}\right)={\displaystyle \frac{8!}{2!(8-2)!}}={\displaystyle \frac{8\cdot 7}{2\cdot 1}}=28 \\ {C}_2(6)=\left({\displaystyle \genfrac{}{}{0px}{}{6}{2}}\right)={\displaystyle \frac{6!}{2!(6-2)!}}={\displaystyle \frac{6\cdot 5}{2\cdot 1}}=15 \\ p={\displaystyle \frac{\left(\genfrac{}{}{0px}{}{8}{2}\right)\cdot \left(\genfrac{}{}{0px}{}{6}{2}\right)}{\left(\genfrac{}{}{0px}{}{8+6}{4}\right)}}={\displaystyle \frac{28\cdot 15}{\left(\genfrac{}{}{0px}{}{8+6}{4}\right)}}={\displaystyle \frac{60}{143}}=0.4196 \end{gathered}$$

Try another example

Related math problems and questions:

• White and black balls
  There are 7 white and 3 black balls in an opaque pocket. The balls are the same size. a) Randomly pull out one ball. What is the probability that it will be white? We pull out one ball, see what color it is and return it to the pocket. Then we pull out th
• One green
  In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
• BW-BS balls
  Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of
• Balls
  From the urn in which are 7 white balls and 17 red, gradually drag 3-times without replacement. What is the probability that pulls balls are in order: red red red?
• Cards
  From a set of 32 cards, we randomly pull out three cards. What is the probability that it will be seven kings and ace?
• Round destiny
  There are 5 white and 10 red balls in the destiny. 4 balls will be drawn at random. What is the probability of the event "at least 2 spheres are white"?
• Components
  In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
• Balls
  We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides
• Green - Red
  We have 5 bags. Each consist one green and 2 red balls. From each we pull just one ball. What is the probability that we doesn't pull any green ball?
• Peaches
  There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
• A box
  A box contains 6 red balls, 5 blue, and 4 white balls. Find the probability of drawing a) red ball b) non-white ball.
• Lord Ram
  When lord Ram founded the breed white sheep was 8 more than black. Currently white sheep are four times higher than at the beginning and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black shee
• Three colors
  Find the probability that 3 balls of the same color will be drawn from fate with 10 white, 10 red, and 10 blue balls.
• Chess pieces
  There are 5 black chess pieces in the box. How many white pieces should we add to this box so that the probability of pulling out a black piece is 1: 4?
• Red balls
  In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
• Cards
  Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
• Family
  94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.