A goldsmith has a bag, which contains some colourful stones. It contains 4 white and 8 black stones. There is another bag which contains 5 white and 5 black stones. One stone is to drawn from either of the two bags. What is the probability of drawing a white stone?Options7/135/1211/128/13
Question
A goldsmith has a bag, which contains some colourful stones. It contains 4 white and 8 black stones. There is another bag which contains 5 white and 5 black stones. One stone is to drawn from either of the two bags. What is the probability of drawing a white stone?Options7/135/1211/128/13
Solution
To solve this problem, we first need to calculate the total probability of drawing a stone from either bag.
-
The probability of choosing either bag is 1/2 (since there are two bags).
-
The probability of drawing a white stone from the first bag is 4/(4+8) = 1/3.
-
The probability of drawing a white stone from the second bag is 5/(5+5) = 1/2.
-
Now, we use the law of total probability to calculate the overall probability of drawing a white stone. This law states that the total probability of an outcome is the sum of its individual probabilities in all possible scenarios.
So, the total probability of drawing a white stone is:
= (probability of choosing the first bag * probability of drawing a white stone from the first bag) + (probability of choosing the second bag * probability of drawing a white stone from the second bag)
= (1/2 * 1/3) + (1/2 * 1/2)
= 1/6 + 1/4
To add these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.
= 2/12 + 3/12
= 5/12
So, the probability of drawing a white stone is 5/12.
Similar Questions
A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing the red marble? Answer options with 5 options A. StartFraction 1 over 144 EndFraction B. StartFraction 1 over 11 EndFraction C. StartFraction 1 over 12 EndFraction D. StartFraction 7 over 12 EndFraction E. StartFraction 27 over 44 EndFraction
9-41. Thu has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part below, if the marble selected is replaced before the next marble is drawn, what is the probability that she will draw.4. A red marble?b. A red or a green marble?An orange marble?
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?Choices:- 3/7 4/7 9/20 8/15
A bag contains 6 red marbles, 5 black marbles and 4 white marbles. Two marbles are drawn from the bag, one after the other, without replacement. If the first marble drawn is red, what is the probability that the second marble drawn is also red.
There are 3 green marbles and 7 orange marbles in a bag.Without looking Jill selected 2 marbles. What is the probability of drawing 2 green marbles? Question 2Select one:a.1/15b.6/100c.6/20d.5/20e.None of these answers are correct
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.