Test: Probability- 4 - Question 10 SaveThere are two bags, one of them contains 5 red and 7 white balls and the other 3 red and 12 white balls, and a ball is to be drawn from one or the other of the two bags. Find the chance of drawing a red ball.
Question
Test: Probability- 4 - Question 10 SaveThere are two bags, one of them contains 5 red and 7 white balls and the other 3 red and 12 white balls, and a ball is to be drawn from one or the other of the two bags. Find the chance of drawing a red ball.
Solution
To solve this problem, we need to use the law of total probability.
Step 1: Calculate the probability of drawing a ball from each bag. Since the problem doesn't specify, we'll assume it's equally likely to draw from either bag. So, the probability of drawing from Bag 1 (P(B1)) is 0.5 and the probability of drawing from Bag 2 (P(B2)) is also 0.5.
Step 2: Calculate the probability of drawing a red ball from each bag. In Bag 1, there are 5 red balls out of a total of 12 balls (5 red + 7 white), so the probability of drawing a red ball from Bag 1 (P(R|B1)) is 5/12. In Bag 2, there are 3 red balls out of a total of 15 balls (3 red + 12 white), so the probability of drawing a red ball from Bag 2 (P(R|B2)) is 3/15 or 1/5.
Step 3: Use the law of total probability to find the overall probability of drawing a red ball. The law of total probability states that P(A) = P(B1)*P(A|B1) + P(B2)*P(A|B2). Substituting in our values, we get P(R) = P(B1)P(R|B1) + P(B2)P(R|B2) = 0.5(5/12) + 0.5(1/5) = 0.2083 + 0.1 = 0.3083.
So, the chance of drawing a red ball is approximately 0.3083 or 30.83%.
Similar Questions
A bag contains 9 blue, 4 black, 5 red and 7 white balls. One ball is taken out of the bag and found to be a red ball then again one ball is taken out at random from the remaining. What is the probability that it will be a white or a red ball?
A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.Choices:- 23/42 19/42 7/32 16/39
Question1: if the box contains six white balls and some red balls and if the probability of drawing a red ball from the box is twice that of a white ball then the number of red balls are*1 pointa) 3b) 6c) 24d) 12Question 2: based on the information given in question ( 1) if two more white balls added in the box , then the probability of drawing a red ball is*1 pointa) 1/2b) 3/5c)2/5d) 4/5Question 3: If the bag contains 5 white balls , 10 blue balls and 5 green balls and if a ball is drawn at random then the probability of not green is1 point3/41/23/51/5Question 4: If the box contains 24 balls each of which is white , brown and yellow. the probability of choosing a white ball at random from the box is 1/6 and the probability of choosing a brown ball at random is 3/8, then the number of yellow ball in the box is1 point20111319
Amy has two bags. Bag I has 7 red and 4 blue balls and bag II has 5 red and 9 blueballs. Amy draws a ball at random and it turns out to be red.Determine the probability that the ball was from the bag I using the Bayes
In a bag, there are 8 red, 10 blue and 12 green balls. A ball is picked randomly from the bag and 5 blue balls are added to the bag. Now, one ball is picked randomly from the bag. What is the probability that the first ball picked is red and the second ball picked is blue?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.