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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
- a)1/90
- b)1/2
- c)19/90
- d)2/9
Correct answer is option 'D'. Can you explain this answer?
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A box contains 5 black and 5 red balls. Two balls are randomly picked ...
The probability of drawing two red balls without replacement
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A box contains 5 black and 5 red balls. Two balls are randomly picked ...
**Problem Solving Approach:**
To solve this problem, we need to find the probability of selecting two red balls from the box.
**Step 1: Determine the Total Number of Outcomes:**
In the given scenario, there are 10 balls in total (5 black and 5 red). When we pick two balls one after another without replacement, the total number of outcomes is determined by the concept of combinations.
The total number of outcomes can be calculated using the formula:
nCr = n! / ((n-r)! * r!)
Where n is the total number of balls and r is the number of balls we need to select.
In this case, n = 10 (total number of balls) and r = 2 (number of balls to be selected).
Total number of outcomes = 10C2 = 10! / ((10-2)! * 2!) = 45
**Step 2: Determine the Number of Favorable Outcomes:**
To find the number of favorable outcomes, we need to determine the number of ways to select two red balls from the five available red balls.
The number of ways to select r items from a set of n items can be calculated using the combination formula:
nCr = n! / ((n-r)! * r!)
In this case, n = 5 (number of red balls) and r = 2 (number of balls to be selected).
Number of favorable outcomes = 5C2 = 5! / ((5-2)! * 2!) = 10
**Step 3: Calculate the Probability:**
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the probability of selecting two red balls is:
Probability = 10 / 45 = 2/9
Therefore, the correct option is d) 2/9.
To solve this problem, we need to find the probability of selecting two red balls from the box.
**Step 1: Determine the Total Number of Outcomes:**
In the given scenario, there are 10 balls in total (5 black and 5 red). When we pick two balls one after another without replacement, the total number of outcomes is determined by the concept of combinations.
The total number of outcomes can be calculated using the formula:
nCr = n! / ((n-r)! * r!)
Where n is the total number of balls and r is the number of balls we need to select.
In this case, n = 10 (total number of balls) and r = 2 (number of balls to be selected).
Total number of outcomes = 10C2 = 10! / ((10-2)! * 2!) = 45
**Step 2: Determine the Number of Favorable Outcomes:**
To find the number of favorable outcomes, we need to determine the number of ways to select two red balls from the five available red balls.
The number of ways to select r items from a set of n items can be calculated using the combination formula:
nCr = n! / ((n-r)! * r!)
In this case, n = 5 (number of red balls) and r = 2 (number of balls to be selected).
Number of favorable outcomes = 5C2 = 5! / ((5-2)! * 2!) = 10
**Step 3: Calculate the Probability:**
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the probability of selecting two red balls is:
Probability = 10 / 45 = 2/9
Therefore, the correct option is d) 2/9.
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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red isa)1/90b)1/2c)19/90d)2/9Correct answer is option 'D'. Can you explain this answer?
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