(a) Let the number of red balls in bag P be 2x, the number of blue balls in bag Q be 3x, and the number of white balls in bag R be 5y. Then, the total number of red balls is 2x, the total number of blue balls is 3x, and the total number of white balls is 5y.
The total number of balls in the big bag is 2x + 3x + 5y = 10y.
Therefore, the probability of picking a red ball is 2x/10y = 2/10 = 1/5.
(b) (i) The probability of picking a white ball and a blue ball with replacement is the probability of picking a white ball multiplied by the probability of picking a blue ball.
For a white ball: 5y/10y = 1/2
For a blue ball: 3x/10y
Therefore, the probability of picking a white ball and a blue ball is (1/2) * (3x/10y) = 3x/20y = 3/(2*10) = 3/20.
(ii) The probability of picking a blue ball first and then a red ball with replacement is the probability of picking a blue ball multiplied by the probability of picking a red ball.
For a blue ball: 3x/10y
For a red ball: 2x/10y
Therefore, the probability of picking a blue ball first and then a red ball is (3x/10y) * (2x/10y) = 6x^2 / 100y^2 = 3 / 25.
Three bags labelled P,Q and R contains red,blue and white balls respectively of equal sizes. The ratio of the balls in the bags are P:Q =2:3 and Q:R=4:5. All the balls are removed into a big bag and properly mixed together. (a)Find the probability of picking a red ball; (b)If two balls are picked at random one after the other with replacement,find the probability of picking: (i)a white ball and a blue ball; (ii)a blue ball first and then a red ball
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