Probability

Q.1 (B)(iii) Two coins are tossed simultaneously. Write the sample space (S) and the number of sample points \(n(S)\).

Q.2 (A)(iii) Complete the following activity to find the probability of getting tail when one coin is tossed.

Activity :

Let ‘S’ be the sample space.
\(S = \{H, T\}\)
\(n(S) = \) ____
Let A be the event of getting tail.
\(A = \{\) ____ \(\}\)
\(\therefore n(A) = \) ____
\(P(A) = \dfrac{n(A)}{n(S)}\)
\(P(A) = \) ____

Q.2 (B)(v) If one die is rolled, then write the sample space (S), \(n(S)\), event A in the set form and \(n(A)\).
Event A : getting odd number on the upper face.

Q.3 (B)(iv) A two digit number is formed using digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is :
(a) an odd number.
(b) a multiple of 5.

Q.1 (B)(iii) When two coins are tossed simultaneously, write the sample space ‘S’.

Q.2 (A)(i) If one die is rolled, then find the probability of the event, that the number on the upper face is prime.

Solution :

‘S’ is the sample space.
S = {1, 2, 3, 4, 5, 6}
\(\therefore n(S) =\) ____
Event A : Prime number on the upper face.
A = {2, 3, 5}
\(\therefore n(A) =\) ____
\(\therefore P(A) = \dfrac{\text{____}}{\text{____}}\)
\(\therefore P(A) = \dfrac{\text{____}}{6}\)
\(= \dfrac{1}{2}\)

Q.2 (B)(i) If two coins are tossed simultaneously, find the probability of the event, “getting at least one head.”

Q.3 (B)(iii) There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that :

(1) The number on the card drawn is a natural number.
(2) The number on the card drawn is a whole number.

Q.1 (A)(iv) Which number cannot represent a probability ?

Q.1 (B)(iv) Two coins are tossed simultaneously. Write the sample space S.

Q.3 (A)(ii) A two digit number is to be formed from the digits 2, 3, 5 without repetition of the digits. Complete the following activity to find the probability that the number so formed is an odd number.

Activity :

Let S be the sample space.
S = {23, 25, 32, ____, 52, 53}
n(S) = ____
Event A : The number so formed is an odd number.
A = {23, 25, ____, 53}
n(A) = 4
P(A) = ____ / n(S) ............ (Formula)
P(A) = ____ / 6
P(A) = ____ / 3.

Q.3 (B)(iii) A committee of two members is to be formed from three boys and two girls. Find the probability of the following events :

Event A : At least one girl must be a member of the committee.
Event B : Committee must be of one boy and one girl.

Q.1 (A)(iv) From the following numbers which number cannot represent a probability ?

Q.3 (A)(ii) A card is drawn from a well shuffled pack of 52 playing cards. Complete the following activity to find the probability of the following events :

(a) A red card

(b) A face card.

Activity :

Let ‘S’ is the sample space

\(\therefore\ n(S) =\) ____

Event A : Card drawn is a red card.

Total red cards = ____

\(\therefore\ n(A) =\) ____

\(\therefore\ P(A) = \dfrac{n(A)}{n(S)}\) ................. Formula

\(\therefore\ P(A) = \dfrac{26}{52}\)

\(\therefore\ P(A) =\) ____

Event B : Card drawn is a face card.

Total face cards = 12

\(\therefore\ n(B) =\) ____

\(\therefore\ P(B) = \dfrac{n(B)}{n(S)}\) ................. Formula

\(\therefore\ P(B) = \dfrac{12}{52}\)

\(\therefore\ P(B) =\) ____

Q.4 (ii) Two dice are thrown. Find the probability of the following events :

(a) Event A : The sum of the numbers on their upper faces is at least 9.

(b) Event B : The sum of the numbers on their upper faces is divisible by 5.

(c) Event C : The number on the upper face of the first die is greater than the number on the upper face of the second die.

Q.1 (A)(iv) Which number from the following cannot represent probability ?

Q.1 (B)(iv) Write sample space if one die is thrown.

Q.3 (A)(ii) The numbers 2, 4, 6, 8, 10, 12 are on the surface of one die. If this die is rolled once, then complete the activity to find probability of getting a number on upper face is a perfect square.

Activity :

S = {____}

\(n(S) = \) ____

Condition for event B : getting a perfect square on the upper surface of that die.

\(\therefore\) B = {____}    \(\therefore n(B) = \) ____

\(P(B) = \dfrac{n(B)}{n(S)} = \dfrac{____}{6} = \) ____

Q.3 (B)(iii) Two dice are rolled. Write the sample space ‘S’ and number of sample points \(n(S)\). Also write the events in the set form and number of sample points in the event according to the given condition.

(a) Condition for event A : Sum of the digits on upper face is a multiple of 5.
(b) Condition for event B : Sum of the digits on upper face is 25.

Q.1 (B)(iv) Two digit numbers are formed using digits 2, 3 and 5 without repeating a digit. Write the sample space.

Q.2 (A)(iii) Two coins are tossed simultaneously. Complete the following activity to write the sample space and the given events A and B in the set form :

Event A : To get at least one head.

Event B : To get no head.

Activity :

Two coins are tossed simultaneously.

\(\therefore\) Sample space is

S = {____, HT, TH, ____}

Event A : To get at least one head.

\(\therefore\) A = {____, HT, TH}

Event B : To get no head.

\(\therefore\) B = {____}

Q.2 (B)(iv) A card is drawn from well shuffled pack of 52 playing cards. Find the probability that the card drawn is a face card.

Q.3 (B)(iv) One coin and a die are thrown simultaneously. Find the probability of the following events :

Event A : To get a head and a prime number.

Event B : To get a tail and an odd number.