## Arithmatical -Probability

DIRECTIONS : Problems based on Probability.
1. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? A.  1/10 B.  2/5 C.  2/7 D.  5/7
Solution
 P(getting a prize) = 10 / (10+25) ‹=› 10 / 35 ‹=› 2 / 7.
2. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? A.  3/4 B.  4/7 C.  1/8 D.  3/7
Solution
 Total number of balls =(6+8) = 14. Number of white balls = 8. P(drawing a white ball) = 8/14 ‹=› 4/7.
3. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? A.  1/15 B.  25/57 C.  35/256 D.  1/221
Solution
 Let S be the sample space. Then, n(S) = 52C2 = (52×51)/(2×1) = 1326. Let E = event of getting 2 kings out of 4. n(E) = 4C2 = (4×4)/(2×1) = 6. P(E) = n(E) / n(S) = 6 / 1326 = 1/221.
4. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5? A.  1/2 B.  2/5 C.  8/15 D.  9/20
Solution
P(E)= n(E) / n(S) Here S=(1,2,3,4,5,...,19,20). Let E=event of getting a multiple of 3 or 5 = (3,6,9,12,15,18,5,10,20) = 9/20.
5. What is the probability of getting a sum 9 from two throws of a dice? A.  1/6 B.  1/8 C.  1/9 D.  1/12
Solution
 In two throws of a die, n(S) = (6×6) = 36. Let E = event of getting a sum 9= {{3,6),(4,5),(5,4),(6,3)} P(E) = n(E) / n(S) = 4/36 ‹=›1/9.
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