**Category : **9th Class

The following are the terms related to describe the concept of probability:

** Event**

The outcomes of a random experiment is called its elementary event. When one coin is tossed, H and T is possible outcome. That is why Getting head is an elementary event. When two coins are tossed, the sample space of this experiment is {HH, HT, TH, TT} Events are HH, HT, TH and TT are the events of random experiment of tossing two coins.

**Compound Events**

When two or more than two elementary events occur with a random experiment, it s said to be Compound Event. When we throw a dice and getting odd number is a compound event.

** Equally Likely Events**

A given number of events are said to be equally likely, if none of them is expected to occur in preference to the others.

If you roll an unbiased dice then each number is equally likely to occur. If a dice is so formed that a particular face occurs most often then the dice is biased. In this case, the outcomes are not equally likely to happen.

** Possible Outcomes**

The total number of the events which are possible to occur is called possible outcomes.

When one dice is thrown, the possible outcomes are {1, 2, 3, 4, 5, 6}

When two dices are thrown , the possible outcomes are {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5,1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}

**Favorable Outcomes**

The outcomes which satisfy the given condition of chance is called favorable outcomes. When an unbiased dice is thrown, the number obtained which is greater than 2 3, 4, 5, 6 are the favorable outcomes.

**Probability of an Event**

Let event is denoted by E the probability of occurrence ratio of event and sample space mathematically. Let the number of events is denoted by n (e) and number of sample space denoted by n(S) then\[P(E)=\frac{n(E)}{n(S)}\]

For examination you have selected 100 question for Preparation. In which 10 question match with exam paper. The probability\[=\frac{10}{100}=\frac{1}{10}\]

** Sure Event**

Sure event is an event whose probability is always one.

** In a single toss of dice, what will be the probability of getting a number which is less then7?**

**Solution:**

Sample space = {1, 2, 3, 4, 5, 6}

\[\therefore \]\[n(E)=6\]

\[\therefore \]\[P(E)=\frac{n(E)}{n(S)}=\frac{6}{6}=1\]. So it is sure event.

**Find the probability of getting head, if the coin is two headed.**

(a) 1

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

(c) \[\frac{1}{3}\]

(d) \[\frac{1}{4}\]

(e) None of these

**Answer:** (a)

**Explanation: **

In two headed coin, sample space = {H, H} number of sample space = 2 =n(s).

\[\therefore \] E be the event of getting head = {H, H}

\[\therefore \]\[n(E)=2\]

\[\therefore \]\[n(E)=\frac{2}{2}=1\].

**Impossible Event **

Impossible event is an event whose probability is 0 (zero).

**If a coin is tossed then what is the probability of getting I?**

**Solution:**

We know that when a coin is tossed, only head or tail will come. There is no any event which is one. Due to this region number of event = 0. Therefore, probability is also zero.

**Note:** From the above calculation we can say that probability of any event lies between 0 and 1. i.e.\[0\le P(E)\le 1\]. It means that maximum probability = 1, and minimum probability = 0. Also, probability can never be negative.

** Complementary Event **

Let E be an event and E' (not E) be an event which occur only when E does not occur. So, E' is called complementary event of E. \[\therefore \] \[P(E)+P({{E}^{1}})=1\] \[\]

**The Probability that it will rain today is 0.84. What is the probability that it will not rain today?**

(a) 0.12

(b) 0.1

(c) 0.3

(d) 0.4

(e) None of these

**Answer:** (e)

**Explanation**

\[P(E)=0.84,\] we know that \[P(E)+P({{E}^{1}})=1\] or \[0.84+P({{E}^{1}})=1,P({{E}^{1}})=-0.84=0.16\]

**What is the probability that an ordinary year has 53 Sunday?**

(a) \[\frac{1}{2}\]

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

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

(d) \[\frac{1}{7}\]

(e) \[\frac{1}{5}\]

**Answer:** (d)

**Explanation**

An ordinary year has 365 days, i.e., 52 weeks and 1 day then PC that this days in Sunday) \[=\frac{1}{7}\]

**Drawing a Card **

We know that there are 52 cards in pack of card.

It is of four types, such as Spades, Clubs, Hearts and Diamonds. All are equally divided. It means that 13 spades, 13 clubs, 13 hearts and 13 diamonds. In 52 cards, there are two colour red and black which is also equally divided. It means that 26 red cards and 26 black cards. Hearts and diamonds are red cards and spades and clubs are black cards.

Name all the 13 cards given below: 2 3, 4, 5, 6, 7, 8, 9, 10, Ace, Jack, King, Queen. The total number of cards are 52. Out of 52 some of the cards are shown below:

**Face Cards**

Kings, queens and jakes are called face cards, therefore, total number of face cards is 12: In which 6 is Red face cards and 6 is black face cards.

**Number Card**

The card on which numbers are written is called number card. 2, 3, 4, 5, 6, 7, 8, 9, 10 are the number cards.

- Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy nowadays, all sciences suggest problems studied by mathematicians, and mar problems arise within mathematics itself.
- The best-known award in mathematics is the Fields Medal established in 1936 and now awarded every 4 years.

- The outcomes of a random experiment is called its elementary event.
- When two or more than two elementary events occurs with random experiment then it is said to be Compound Event.
- The outcomes which satisfies the given condition of chance is called favorable outcomes.
- \[P(E)=\frac{n(E)}{n(S)}\] v \[P(E)+P(\overline{E})=1\]

**One card is drawn from a well shuffled deck of 52 cards. What is the probability of getting a black face card?**

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

(b) \[\frac{3}{14}\]

(c) \[\frac{3}{26}\]

(d) \[\frac{3}{13}\]

(e) None of these

**Answer:** (c)

**Explanation **

Number of black face card = (2 king + 2 queen + 2 jack) = 6.

\[\therefore \]\[P(E)=\frac{6}{52}=\frac{3}{26}\]

**There are 20 tickets numbered as 1, 2, 3 -? 20 respectively one ticket is drawn at random. What is the probability that the number on the ticket is a multiple of 3 or 5?**

(a) \[\frac{1}{4}\]

(b) \[\frac{1}{5}\]

(c) \[\frac{2}{5}\]

(d) \[\frac{4}{10}\]

(e) None of these

**Answer:** (b)

**There are 25 cards numbered as 1, 2, 3, ---25 respectively one card is drawn at random. What is the probability that the number on the card is a multiple of 4 or 5?**

(a) \[\frac{2}{5}\]

(b) \[\frac{11}{25}\]

(c) \[\frac{12}{25}\]

(d) \[\frac{13}{25}\]

(e) None of these

**Answer:** (b)

**A cartoon contains 144 bulbs out of which 20 are defective and others are good. Peter will buy one bulb if it is good, but will not buy if it is defective. The shopkeeper draws one bulb at random and gives it to him. The probability that he will buy it?**

(a) \[\frac{5}{36}\]

(b) \[\frac{31}{36}\]

(c) \[\frac{13}{36}\]

(d) \[\frac{15}{36}\]

(e) None of these

**Answer:** (b)

** In a class, there are 20 boys and 18 girls. The class teacher wants to choose one student as class representative. He writes the name of each student on a flash card and puts them into a bag and mixes it. A student picks one card from the bag. Find the probability that the name written on the card is the name of a girl.**

(a) \[\frac{8}{19}\]

(b) \[\frac{6}{19}\]

(c) \[\frac{7}{19}\]

(d) \[\frac{9}{19}\]

(e) None of these

**Answer:** (d)

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