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A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is
A
$$\frac{1}{3}$$
B
$$\frac{3}{7}$$
C
$$\frac{1}{2}$$
D
$$\frac{4}{7}$$
Correct Answer:
$$\frac{1}{2}$$
Directions: Seven different boxes A, B, C, D, E, F and G of different colours viz., Orange, Pink, Purple, Yellow, Blue, Red and Green are arranged one above the other. The box at the bottom of arrangement is numbered 1, the above box is numbered 2 and so on. B is immediately above E. More than two boxes are above the Orange box. The Yellow box is immediately below A. Only one box is between the Orange box and F. G is immediately above the Red box. Only one box is between B and the Pink box. Only two boxes are between the Pink and the Green box. Only two boxes are between the Yellow box and the Orange box. The Purple box is neither at the top nor at the bottom of the arrangement.B is above Pink box. C is immediately above F. Neither C nor G is a Yellow box. G is not a Orange box. Question: Which combination represents the position of C and its colour?
A
6-Green
B
6-Red
C
5-Purple
D
7-Blue
A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
A
$$\frac{1}{{20}}$$
B
$$\frac{1}{{12}}$$
C
$$\frac{3}{{10}}$$
D
$$\frac{1}{2}$$
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is
A
$$\frac{4}{{15}}$$
B
$$\frac{7}{{16}}$$
C
$$\frac{1}{2}$$
D
$$\frac{8}{{15}}$$
A box contains 5 white balls and 3 red balls. Two balls are withdrawn from the box randomly, one after another (without replacement). The probability that the two balls withdrawn are of different colour is
A
$$\frac{{15}}{{64}}$$
B
$$\frac{{25}}{{64}}$$
C
$$\frac{{25}}{{56}}$$
D
$$\frac{{30}}{{56}}$$
A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.
A
23\/42
B
19\/42
C
7\/32
D
16\/39
Statements followed by some conclusions are given below. Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 2 balls are selected at random from the bag. Conclusions:
1. The probability that a black ball is selected is 1/5.
2. The probability that a red ball is selected is 6/15. Find which of the conclusions logically follows from the given statements.
A
Only conclusion 1 follows
B
Only conclusion 2 follows
C
Both 1 and 2 follow
D
Neither 1 nor 2 follows
In a bag which contains 40 balls, there are 18 red balls and some green and blue balls. If two balls are picked up from the bag without replacement, then the probability of the first ball being red and second being green is 3/26. Find the number of blue balls in the bag.
A
16
B
12
C
10
D
14
A bag contains 6 red balls 11 yellow balls and 5 pink balls. If two balls are drawn at random from the bag. One after another what is the probability that the first ball is red and second ball is yellow?
A
$$\frac{1}{14}$$
B
$$\frac{2}{7}$$
C
$$\frac{1}{7}$$
D
$$\frac{3}{14}$$
E
None of these
A bag contains 4 red balls, 6 blue balls and 8 pink balls. One ball is drawn at random and replaced with 3 pink balls. A probability that the first ball drawn was either red or blue in colour and the second drawn was pink in colour ?
A
$$\frac{12}{21}$$
B
$$\frac{13}{17}$$
C
$$\frac{11}{30}$$
D
$$\frac{13}{18}$$
E
None of these
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
A
$$\frac{1}{{90}}$$
B
$$\frac{1}{2}$$
C
$$\frac{{19}}{{90}}$$
D
$$\frac{2}{9}$$