a bag contains 7 white balls and 9 black balls. two balls are drawn in succession at random. what is the probability that one of them is white and other black.
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Step-by-step explanation:
numbers of white balls n(w) : 7
numbers of black balls n(b) : 9
total numbers of balls : 7+9
n(s) : 16 balls
A bag contains 7 white and 9 black balls, 2 balls are drawn in successive at random? What is prob one of them is white and the other one is black?
Indian students are only aware of 7 out of 250+ career options.
There are total 16 balls , 7-white and 9-black , you want the prob one is white and one is black , there will be 2 cases,
Case 1 : 1st ball - white and 2nd ball - Black ;
Probability = 7/16*9/15 = 0.2625
Case 2 : 1st ball - black and 2nd ball - white;
Probability = 9/16*7/15 = 0.2625
Prob of Case 1+ prob of Case 2 = 0.2625+0.2625 = 0.525.
Another way to solve it is creating sample space , in this case the sample space is small , so we can create sample space , for few sums we cannot because sample space can be very large and calculation will be difficult.
In this case sample space is ( BB , BW, WW, WB) [ B = black , W = white]
we need only black and white therefore there only possible option among the sample space , so
probability will be = 2/4 = 1/2
Rougly 50 %.
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