A bag Contains 10Red and 6 green Balls and 4 successive draws are made without replaceemat and with replacement .find the probability that they are alternatively of same?
Answers
Answer:
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Concept
Probability is basically the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Given
There are 10 red balls,6 green balls and 6 green balls in the bag.
To find
The probability of getting all same when 4 balls are drawn with and without replacement.
Explanation
Number of red balls=10
Number of green balls=6
let X draws the colour of ball.
Probability=Number of items/ total items
- When ball is replaced.
When a ball is replaced means the number of balls in the bag will not reduce.
Probability of getting same=
P(X=Red)*P(X=Red)*P(X=Red)*P(X=Red)+P(X=Green)*P(X=Green)*P(X=Green)*P(X=Green)
=10/16*10/16*10/16*10/16+6/16*6/16*6/16*6/16
=10000/65536+1296/65536
=11296/65536
=0.1723
- When ball is not replaced.
When the ball is not replaced means the number of balls in the bag will reduce.
Probability of getting same=
P(X=Red)*P(X=Red)*P(X=Red)*P(X=Red)+P(X=Green)*P(X=Green)*P(X=Green)*P(X=Green)
=10/16*9/15*8/14*7/13+6/16*5/15*4/14*3/13
=5040/43680+360/43680
=5400/43680
=0.1236
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