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**ADDITIONAL QUESTIONS SOLVED**

**VERY SHORT ANSWER TYPE QUESTIONS**

**Q1. A letter is chosen at random from English alphabet. Find the probability that the letter chosen precedes â€˜gâ€™.**

**Sol. **Total number of letters in English alphabet is 26.

âˆ´ Total number of possible outcomes = 26

âˆµ Letters preceding â€˜gâ€™ are:

a, b, c, d, e and f

âˆ´ Favourable outcomes = 6

**Q2. A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant.**

**Sol.** There are 26 letters in English alphabets.

â‡’ Possible outcomes = 26

âˆµ There are 5 vowels (a, e, i, o, u) and remaining are consonants.

âˆ´ Number of consonants = 26 â€“ 5 = 21

â‡’ Favourable outcomes = 21

âˆ´ P(consonants) = 21/16

**Q3. A bag contains 9 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is black?**

**Sol. **Total number of balls = 9 + 12 = 21

â‡’ Number of possible outcomes = 21

Number of black balls = 9

â‡’ Number of favourable outcomes = 9

âˆ´ Required probability = 9/21 = 3/7.

**Q4. Find the probability that a number selected from the numbers 1 to 25 which is not a prime number when each of the given number is equally likely to be selected.**

**Sol.** Total number of given numbers = 25

Since the numbers 2, 3, 5, 7, 11, 13, 17, 19 and 23 are prime number.

There are 9 numbers.

âˆ´ Number of numbers that are not prime = 25 âˆ’ 9 = 16

âˆ´ Number of favourable outcomes = 16

â‡’ Required probability = 16/25.

**Q5. A die is thrown once. Find the probability of getting an odd number.**

**Sol. **Total number of possible outcomes = 6

[âˆµ Numbers 1 to 6 are marked on the faces of a die]

âˆµ odd numbers are 1, 3 and 5

âˆ´ Favourable outcomes = 3

âˆ´ Required probability = 3/6 = 1/2.

**Q6. Cards each marked with one of the numbers 6, 7, 8, ....., 15 and placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with number less than 10?**

**Sol.** âˆµ There are 10 cards. âˆ´ Total number of possible outcomes = 10

Cards marked with a number less than 10 are: 6, 7, 8 and 9

i.e. The number of favourable outcomes = 4

**Q7. A card is drawn at random from a wellshuffled deck of 52 cards. What is the probability of getting a black king?**

**Sol. **âˆµ Total number of cards = 52

âˆ´ Number of possible outcomes = 52

Number of black king = 2

**Q8. What is the probability that two different friends have different birthdays? (Ignoring leap year).**

**Sol**. Number of days in a year = 365

â‡’ Number of possible outcomes = 365

Since they have different birthdays.

âˆ´ Number of favourable outcomes = 365 âˆ’ 1 = 364

**Q9. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?**

**Sol.** Total number of balls = 3 + 2 + 4 = 9

âˆ´ Number of possible outcomes = 9

Since, number of white balls = 2

âˆ´ Number of balls which are not white = 9 âˆ’ 2 = 7

â‡’ Number of favourable outcomes = 7

âˆ´ P(E) = 7/9.

**Q10. From a well-shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.**

**Sol.** âˆµ Total number of cards = 52

Since, the number of black queens = 2

âˆ´ Number of favourable outcomes = 2

**Q11. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. Find the probability of getting a black ball.**

**Sol.** Total number of balls = 4 + 6 = 10

â‡’ All possible outcomes = 10

Since, number of black balls = 6

âˆ´ Number of favourable outcomes = 6

**Q13. A die is thrown once. Find the probability of getting a number greater than 5.**

**Sol.** Total number of possible outcomes = 6

Since only one number i.e., 6 is greater than 5

âˆ´ Favourable number of outcomes = 1

â‡’ P(E) = 1/6.

**Q14. Find the probability of obtaining 7 on a single toss of one die.**

**Sol. **Numbers marked on a die are:

âˆ´ There are six different possible outcomes.

But none of these outcomes would produce a 7.

â‡’ Favouable outcome = 0

âˆ´ P(7) = 0/6 = 0.

When an event cannot possibly succeed, we say it is an impossible event and probability of an impossible event is zero. i.e. P(impossible event) = 0

**Q15. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. What is the probability that the number on the card taken out is an even number? **

**Sol.** Total number of cards (3 to 20) = 18

âˆ´ Number of possible outcomes = 18

Since cards having even numbers (4, 6, 8, 10, 12, 14, 16, 18 and 20) are 9,

âˆ´ Number of favourable outcomes = 9

**Q16. Two friends were born in the year 2000. What is the probability that they have the same birthday ?**

**Sol.** Since the year 2000 was a leap year,

âˆ´ Total number of days in the year = 366

âˆµ They have the same birthday.

âˆ´ Number of favourable outcomes = 1

â‡’ P(E) = 1/36.

**Q17. A box contains cards marked with numbers 5 to 20. A card is drawn from the bag at random. Find the probability of getting a number which is a perfact square**.

**Sol. **âˆµ Total number of cards = 16

âˆ´ Possible outcomes are 16.

Since the numbers 9 and 16 are perfect numbers,

â‡’ Number of favourable outcomes = 2

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