Long Questions: Probability

# Class 10 Maths Chapter 14 Question Answers - Probability

Q1: A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is
(i) a card of spade or an ace.
(ii) a black king.
(iii) neither a jack nor a king.
(iv) either a king or a queen.
Ans:
Total no. of outcomes = 52

Q2: Five cards, the ten, jack, queen, king and ace of diamonds, are well shuffled with their faces downwards. One card is then picked up at random.
(a) What is the probability that the drawn card is the queen?
(b) If the queen is drawn and put aside, and a second card is drawn, find the probability that the second card is (i) an ace (ii) a queen.
Ans: (a)
Total events = 5; P(queen) = 1y/5
(b) Now total events = 4
(i) P (an ace) = 1/4
(ii) P (a queen) = 0/4 = 0 …[As there is no queen left]

Q3: All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) of red colour
(ii) a queen
(iii) an ace
(iv) a face card
Ans:
Total number of cards = 52
Red face cards = 6
Remaining cards = 52 – 6 = 46

Q4: Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) a king
(ii) of red colour
(iii) a face card
(iv) a queen
Ans:

Number of red queens = 2
Number of black jacks = 2
Remaining cards = 52 – 2 – 2 = 48

Q5: Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is:
(i) an odd number
(ii) a perfect square number
(iii) divisible by 5
(iv) a prime number less than 20
Ans:
Total number of cards = 60 – 11 + 1 = 50
(i) Odd nos, are 11, 13, 15, 17, …. 59 = 25 no.
∴ P(an odd number) = 25/50 = 1/2
(ii) Perfect square numbers are 16, 25, 36, 49 = 4 numbers
∴ P(a perfect square no.) = 4/50 = 225
(iii) “Divisible by 5” numbers are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, = 10 numbers
∴ P(divisible by 5) = 10/50 = 2/25
(iv) Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19 = 8 numbers
∴ P(a prime no. less than 20) = 8/50 = 4/25

Q6: All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a:
(i) face card
(ii) red card
(iii) black card
(iv) king
Ans:
Total number of cards = 52
Black face cards = 6
Remaining cards = 52 – 6 = 46

Q7: Red kings and black aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card.
(ii) a red card.
Ans:
Total nos. of cards = 52
Cards removed = 2 + 2 = 4
Remaining cards = 52 – 4 = 48

Q8: All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card.
(ii) a red card.
Ans:
Total no. of cards = 52
No. of cards removed = (4 + 4 + 4) = 12
Remaining cards = 40

Q9: A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) the queen of diamonds.
Ans:
(i)
Total cards in a deck = 52
Total no. of kings = 4
Total no. of red kings = 2

Q10:  Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product.
Ans:
Two dice can be thrown as 6 × 6 = 36 ways.

The document Class 10 Maths Chapter 14 Question Answers - Probability is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Class 10 Maths Chapter 14 Question Answers - Probability

 1. What is probability?
Ans. Probability is a branch of mathematics that deals with the study of uncertainty and the likelihood of events occurring. It quantifies the chances of different outcomes happening and is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
 2. How is probability calculated?
Ans. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio gives us the probability of a specific event occurring. For example, if we want to find the probability of rolling a 6 on a fair six-sided die, we would divide the number of favorable outcomes (1) by the total number of possible outcomes (6), resulting in a probability of 1/6.
 3. What are the different types of probability?
Ans. There are three types of probability: theoretical probability, experimental probability, and subjective probability. - Theoretical probability is based on mathematical calculations using known information. - Experimental probability is determined through repeated experiments or observations. - Subjective probability is based on personal judgment or opinions.
 4. What is the difference between independent and dependent events in probability?
Ans. In probability, independent events are events that do not affect each other's probabilities. The occurrence of one event does not influence the occurrence of the other. For example, flipping a fair coin twice would be an independent event because the outcome of the first flip does not impact the outcome of the second flip. On the other hand, dependent events are events where the outcome of one event affects the probability of the other event. For example, drawing two cards from a deck without replacement would be a dependent event because the probability of drawing a certain card for the second draw depends on the outcome of the first draw.
 5. How can probability be used in real-life situations?
Ans. Probability is widely used in various real-life situations. Here are a few examples: - Weather forecasting: Meteorologists use probability to predict the chances of rain, snow, or other weather conditions. - Insurance: Insurance companies use probability to calculate premiums based on the likelihood of certain events, such as accidents or natural disasters. - Sports: Coaches and players use probability to strategize and make decisions based on the likelihood of certain outcomes, such as scoring a goal or winning a game. - Stock market: Investors use probability to assess the risks and potential returns of different investment options. - Medical research: Probability is used in clinical trials to determine the effectiveness of new drugs or treatments.

## Mathematics (Maths) Class 10

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