A basket contains 3 red balls 5 blue balls and 7 green balls. Two balls are picked one after the other without replacement find the probability that. (a) Both are red. (b) First is blue, the other is green. (c) One is blue, the other is green. (d) Both are of different colours. (e) They are of the same colours.
There are 15 balls in all, so
P(red,red) = 3/15 * 2/14 = 1/35
what do you get for the others?
Probability questions
A certain ore contains 9 percent gold. How much ore (in tons) is needed to obtain 126 tons of gold?
pls ans them
Pls explain better in full please
To find the probabilities, we need to calculate the number of favorable outcomes (picking the specific balls) and divide it by the total number of possible outcomes (picking any two balls from the basket).
Let's start with Part (a), finding the probability that both balls are red:
Step 1: Calculate the number of favorable outcomes.
Since there are 3 red balls in the basket, the number of ways to choose 2 red balls is given by the combination formula: C(3, 2) = 3.
Step 2: Calculate the total number of possible outcomes.
We need to choose 2 balls from a total of 3 red balls, 5 blue balls, and 7 green balls. So, the total number of possible outcomes is given by the combination formula: C(15, 2) = 105.
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
P(Both are red) = 3/105 = 1/35
So, the probability that both balls are red is 1/35.
Moving on to Part (b), finding the probability that the first is blue and the other is green:
Step 1: Calculate the number of favorable outcomes.
We have 5 blue balls to choose from and 7 green balls to choose from for the second pick. So, the number of favorable outcomes is 5 * 7 = 35.
Step 2: Calculate the total number of possible outcomes.
We need to choose 2 balls from a total of 3 red balls, 5 blue balls, and 7 green balls. So, the total number of possible outcomes is C(15, 2) = 105.
Step 3: Calculate the probability.
P(First is blue, the other is green) = 35/105 = 1/3
So, the probability that the first ball is blue and the other is green is 1/3.
Let's move on to Part (c), finding the probability that one is blue and the other is green:
Step 1: Calculate the number of favorable outcomes.
Similar to Part (b), the number of ways to choose one blue ball from 5 and one green ball from 7 is 5 * 7 = 35.
Step 2: Calculate the total number of possible outcomes (same as Parts a and b).
The total number of possible outcomes is C(15, 2) = 105.
Step 3: Calculate the probability.
P(One is blue, the other is green) = 35/105 = 1/3
So, the probability that one ball is blue and the other is green is 1/3.
Moving on to Part (d), finding the probability that both balls are of different colors:
Step 1: Calculate the number of favorable outcomes.
We need to choose one ball from 5 blue balls and one ball from 7 green balls. So, the number of favorable outcomes is 5 * 7 = 35.
Step 2: Calculate the total number of possible outcomes.
The total number of possible outcomes is C(15, 2) = 105 (same as Parts a, b, and c).
Step 3: Calculate the probability.
P(Both are of different colors) = 35/105 = 1/3
So, the probability that both balls are of different colors is 1/3.
Finally, let's move on to Part (e), finding the probability that both balls are of the same color:
Step 1: Calculate the number of favorable outcomes for each color.
For red balls, there are C(3, 2) = 3 favorable outcomes.
For blue balls, there are C(5, 2) = 10 favorable outcomes.
For green balls, there are C(7, 2) = 21 favorable outcomes.
Step 2: Calculate the total number of possible outcomes.
The total number of possible outcomes is C(15, 2) = 105 (same as Parts a, b, c, and d).
Step 3: Calculate the probability.
P(Both are of the same color) = (3 + 10 + 21)/105 = 34/105
So, the probability that both balls are of the same color is 34/105.