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June 23, 2019
Question 1
A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.
1/2
7/5
8/15
1/9
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Let S be the sample space Then n(S) = no of ways of drawing 2 balls out of (6+4) =10C2 10 =10*9/2*1 =45 Let E = event of getting both balls of same colour Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4) =6C2+4C2 = 6*5/2*1+4*3/2*1 = 15+6 = 21 Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
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Question 2
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
3/5
9/20
Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20.
Question 3
Two dice are tossed. The probability that the total score is a prime number is:
5/2
1/6
7/9
Clearly, n(S) = (6 x 6) = 36. Let E = Event that the sum is a prime number. Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4,3),(5, 2), (5, 6), (6, 1), (6, 5) } n(E) = 15. P(E) = n(E)/n(S) = 15/36 = 5/12.
Question 4
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
2/91
1/22
3/22
2/77
Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C3 =(15*14*13)/(3*2*1)= 455. Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5*4/2*1 = 10. => P(E) = n(E)/n(S) = 10/455 = 2/91.
Question 5
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
2/7
5/7
1/5
Total number of outcomes possible, n(S) = 10 + 25 = 35 Total number of prizes, n(E) = 10 P(E)=n(E)/n(S)=10/35=2/7
Question 6
What is the probability of getting 53 Mondays in a leap year?
1/7
3/7
1
1 year = 365 days . A leap year has 366 days A year has 52 weeks. Hence there will be 52 Sundays for sure. 52 weeks = 52 x 7 = 364days 366 – 364 = 2 days In a leap year there will be 52 Sundays and 2 days will be left. These 2 days can be: 1. Sunday, Monday 2. Monday, Tuesday 3. Tuesday, Wednesday 4. Wednesday, Thursday 5. Thursday, Friday 6. Friday, Saturday 7. Saturday, Sunday Of these total 7 outcomes, the favourable outcomes are 2. Hence the probability of getting 53 days = 2/7
Question 7
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
3/13
1/13
3/52
9/52
Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12/52=3/13.
Question 8
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
3/20
29/34
47/100
13/102
Let S be the sample space. Then, n(S) = 52C2=(52 x 51)/(2 x 1) = 1326. Let E = event of getting 1 spade and 1 heart. n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = 13C1*13C1 = 169. P(E) = n(E)/n(S) = 169/1326 = 13/102.
Question 9
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?
4/7
1/8
3/4
Let number of balls = (6 + 8) = 14. Number of white balls = 8. P (drawing a white ball) = 8 /14 = 4/7.
Question 10
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?
1/3
1/4
P(first letter is not vowel) = 24 P(second letter is not vowel) = 1/3 So, probability that none of letters would be vowels is = 2/4×1/3=1/6
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