a bag contains 7 red 5 Blue Balls A ball is taken random from the bag its colour is noted and not replace into the bag now second ball colour is noted find the probability that is one is red and other is blue
Answers
Step-by-step explanation:
is it total question
or any other points are there??
The probability that one ball drawn is red and the other is blue, without replacement, is 35 / 66.
• Given,
Number of red balls in the bag = 7
Number of blue balls in the bag = 5
Total number of balls = 7 + 5 = 12
(i) Case 1 : Probability of drawing a red ball first
Probability of drawing a red ball in the first turn = 7 / 12
Remaining number of balls = 12 - 1 = 11
• According to the question, if a red ball is drawn in the first draw, then a blue ball will be taken out in the second draw.
• Probability of drawing a blue ball in the second turn = 5 / 11
• Therefore, probability of drawing a red ball, followed by a blue ball (P1) = ( 7 / 12 ) × ( 5 / 11 )
= 35 / 132
(ii) Case 2 : Probability of drawing a blue ball first
Probability of drawing a blue ball in the first turn = 5 / 12
Remaining number of balls = 12 - 1 = 11
• According to the question, if a blue ball is drawn in the first draw, then a red ball will be taken out in the second draw.
• Probability of drawing a red ball in the second turn = 7 / 11
• Therefore, probability of drawing a blue ball, followed by a red ball (P2) = ( 5 / 12 ) × ( 7 / 11 )
= 35 / 132
• Probability of either case 1 or case 2 being true = P1 + P2
= ( 35 / 132 ) + ( 35 / 132 )
= ( 35 + 35 ) / 132
= 70 / 132
= 35 / 66
∴ The probability of drawing two different coloured balls in two turns is 35 / 66.