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A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ______.
- a)45/236
- b)1/4
- c)3/16
- d)3/4
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A box contains 15 blue balls and 45 black balls. If 2 balls are select...
Solution:
Given,
Number of Blue balls, B = 15
Number of Black balls, K = 45
Total number of balls, n = B + K = 60
We need to find the probability of selecting one blue ball and one black ball without replacement.
Probability of selecting a blue ball in the first draw = B/n
As one blue ball has already been removed from the box, the number of balls left = n-1.
Probability of selecting a black ball in the second draw given that a blue ball was selected in the first draw = K/(n-1)
The probability of both events occurring is the product of both probabilities, i.e.,
P = (B/n) × (K/(n-1))
Substituting the given values, we get
P = (15/60) × (45/59)
= 45/236
Therefore, the probability of selecting one blue ball and one black ball without replacement is 45/236.
Given,
Number of Blue balls, B = 15
Number of Black balls, K = 45
Total number of balls, n = B + K = 60
We need to find the probability of selecting one blue ball and one black ball without replacement.
Probability of selecting a blue ball in the first draw = B/n
As one blue ball has already been removed from the box, the number of balls left = n-1.
Probability of selecting a black ball in the second draw given that a blue ball was selected in the first draw = K/(n-1)
The probability of both events occurring is the product of both probabilities, i.e.,
P = (B/n) × (K/(n-1))
Substituting the given values, we get
P = (15/60) × (45/59)
= 45/236
Therefore, the probability of selecting one blue ball and one black ball without replacement is 45/236.
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Community Answer
A box contains 15 blue balls and 45 black balls. If 2 balls are select...
Concept:
P(E) = Number of favorable outcomes / Total number of outcomes
Calculation:
Given:
Number of blue balls = 15, Number of black balls = 45
Total number of balls = 15 + 45 = 60 balls
Balls are drawn from the box at random without replacement.
The probability of drawing first blue ball and second black ball is;
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