Jharkhand Board JAC Class 9 Maths Important Questions Chapter 15 Probability Important Questions and Answers.

## JAC Board Class 9th Maths Important Questions Chapter 15 Probability

Question 1.

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) A king.

(ii) A heart.

(iii) A seven of heart.

(iv) A jack, queen or a king.

(v) A two of heart or a two of diamond.

(vi) A face card.

(vii) A black card.

(viii) Neither a heart nor a king,

(ix) Neither an ace nor a king.

Solution :

Total number of outcomes = 52

(i) A king

No. of kings = 4

P(A) = \(\frac{4}{52}=\frac{1}{13}\)

(ii) A heart, P(A) = \(\frac{13}{52}=\frac{1}{4}\)

(iii) A seven of heart P(A) = \(\frac{1}{52}\)

(iv) A jack, queen or a king,

P(A) = \(\frac{12}{52}=\frac{3}{13}\)

(v) A two of heat or a two of diamond,

P(A) = \(\frac{2}{52}=\frac{1}{26}\)

(vi) A face card, P(A) = \(\frac{12}{52}=\frac{3}{13}\)

(vii) A black card, P(A) = \(\frac{26}{52}=\frac{1}{2}\)

(viii) Neither a heart nor a king (13 heart + 4 king, but 1 common)

P(A) = 1 – \(\frac{16}{52}=\frac{52-16}{52}=\frac{36}{52}=\frac{9}{13}\)

(ix) Neither an ace nor a king,

P(A) = \(\frac{44}{52}=\frac{11}{13}\)

Question 2.

Two coins are tossed simultaneously. Find the probability of getting

(i) two heads

(ii) at least one head

(iii) no head

Solution :

On tossing two coins simultaneously, all the possible outcomes are HH, HT, TH, TT.

(i) The probability of getting two heads

= P (HH)

= No. of outcomes of two heads / Total no. of possible outcomes

= \(\frac {1}{4}\)

(ii) The probability of getting at least one head

= No. of favourable outcomes / Total no. of outcomes

= \(\frac {3}{4}\)

(iii) The probability of getting no head

P(TT) = \(\frac {1}{4}\)

Question 3.

A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is

(i) Black

(ii) Not red

(iii) Green

Solution :

Number of red balls in the bag = 5.

Number of white balls in the bag = 8.

Number of green balls in the bag = 4.

Number of black balls in the bag = 7.

∴ Total number of balls in the bag = 5 + 8 + 4 + 7 = 24.

Drawing balls randomly are equally likely outcomes.

∴ Total number of possible outcomes = 24.

Now,

(i) There are 7 black balls, hence the number of such favourable outcomes = 7

∴ Probability of drawing a black ball

= No. of favourable outcomes / Total no. of possible outcomes

= \(\frac {7}{24}\)

(ii) There are 5 red balls, hence the number of such favourable outcomes = 5.

∴ Probability of drawing a red ball

= No. of favourable outcomes / Total no. of possible outcomes

= \(\frac {5}{24}\)

∴ Probability of drawing not a red ball = P(Not red ball) = 1 – \(\frac{5}{24}=\frac{19}{24}\)

(iii) There are 4 green balls.

∴ Number of such favourable outcomes = 4

Probability of drawing a green ball = No. of favourable outcomes / Total no. of possible outcomes

= \(\frac{4}{24}=\frac{1}{6}\)

Question 4.

A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing

(i) a face card

(ii) a red face card

Solution :

Random drawing of cards ensures equally likely outcomes

(i) Number of face cards (King, Queen and jack of each suits) = 4 x 3 = 12.

Total number of cards in deck = 52.

∴ Total number of possible outcomes = 52.

P (drawing a face card) = \(\frac{12}{52}=\frac{3}{13}\)

(ii) Number of red face cards = 2 × 3 = 6.

Number of favourable outcomes of drawing red face card = 6.

P(drawing of red face card) = \(\frac{6}{52}=\frac{3}{26}\)

Multiple Choice Questions

Question 1.

3 Coins are tossed simultaneously. The probability of getting at least 2 heads is

(a) \(\frac {3}{10}\)

(b) \(\frac {3}{4}\)

(c) \(\frac {3}{8}\)

(d) \(\frac {1}{2}\)

Solution :

(c) \(\frac {3}{8}\)

Question 2.

Two cards are drawn successively with replacement from a pack of 52 cards. The probability of getting two aces is

(a) \(\frac {1}{169}\)

(b) \(\frac {1}{221}\)

(c) \(\frac {1}{265}\)

(d) \(\frac {1}{663}\)

Solution :

(b) \(\frac {1}{221}\)

Question 3.

In a single throw of two dice, the probability of getting a sum of more than 7 is

(a) \(\frac {7}{36}\)

(b) \(\frac {7}{12}\)

(c) \(\frac {5}{12}\)

(d) \(\frac {5}{36}\)

Solution :

(c) \(\frac {5}{12}\)

Question 4.

Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is

(a) \(\frac {1}{26}\)

(b) \(\frac {1}{4}\)

(c) \(\frac {1}{17}\)

(d) None of these

Solution :

(c) \(\frac {1}{17}\)

Question 5.

Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is

(a) \(\frac {1}{9}\)

(b) \(\frac {1}{3}\)

(c) \(\frac {1}{4}\)

(d) \(\frac {5}{9}\)

Solution :

(c) \(\frac {1}{4}\)

Question 6.

If the three coins are simultaneously tossed compute the probability of 2 heads coming up.

(a) \(\frac {3}{8}\)

(b) \(\frac {1}{4}\)

(c) \(\frac {5}{8}\)

(d) \(\frac {3}{4}\)

Solution :

(a) \(\frac {3}{8}\)

Question 7.

A coin is tossed successively three times. The probability of getting one head or two heads is:

(a) \(\frac {2}{3}\)

(b) \(\frac {3}{4}\)

(c) \(\frac {4}{9}\)

(d) \(\frac {1}{9}\)

Solution :

(b) \(\frac {3}{4}\)

Question 8.

One card is drawn from a pack of 52 cards. What is the probability that the drawn card is either red or king:

(a) \(\frac {15}{26}\)

(b) \(\frac {1}{2}\)

(c) \(\frac {7}{13}\)

(d) \(\frac {17}{32}\)

Solution :

(c) \(\frac {7}{13}\)