3 Marks Question

Question 13 Marks

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 :
Let S be the sample space.
$\therefore S=\{23,25,32, ⬜, 52,53\}$$\quad$$\quad$$\therefore n(S)$ = ⬜
Now condition of event A is that number so formed is an odd number.
$\therefore A=\{23,25,⬜, 53\}$$\quad$$\quad$ $\therefore n(A)=4$
$\therefore P(A)=\frac{⬜}{n(S)}$$\quad$$\quad$...(Formula)
$\therefore P(A)=\frac{⬜}{6}$
$\therefore P(A)=\frac{⬜}{3}$

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Question 23 Marks

A card is drawn at random from a pack of well-shuffled 52 playing cards. Complete the following activity to find the probability that the card drawn is
(i) an ace(Event A)(ii) a spade (Event B).
S is the sample space.
$\therefore n(S)=52$
(i) Event A: The card drawn is an ace.
$\therefore n(A)$ = ⬜
$P(A)$ = ⬜$\quad$$\quad$...(Formula)
$\therefore P(A)=\frac{⬜}{52}$$\quad$$\quad$$\therefore P(A)=\frac{⬜}{13}$
(ii) Event B: The card drawn is a spade.
$\therefore n(B)$ = ⬜
$P(B)=\frac{n(B)}{n(S)}$
$\therefore P(B)=\frac{⬜}{4}$

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Question 33 Marks

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.

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Question 43 Marks

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.
$\therefore S=\{23,25,32,$ ⬜, $52,53\} $
$\therefore n(S)=$ ⬜
Event A : The number so formed is an odd number.
$\therefore A=\{23,25, $ ⬜, $53\} $
$\therefore n(A)=4 $
$\therefore P(A)=\frac{⬜}{n(S)} ...... ..(\text {Formula}) $
$\therefore P(A)=\frac{⬜}{6} $
$\therefore P(A)=\frac{⬜}{3} .$

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Question 53 Marks

Two-digit numbers are formed from the digits 0, 1, 2, 3. Repetition of the digits are allowed. Complete the following activity to find the probability that the number so formed is a prime number:
The sample space
$S$ = {______}$\quad$$\quad$$\therefore n(S)$=⬜
Let A be the event that the number so formed is a prime number.
$A=$ {______}$\quad$$\quad$$\therefore n(A)$=⬜
$P(A)=\frac{n(A)}{n(S)}$$\quad$$\quad$$\therefore P(A)$=$[-]$=$[-]$

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Question 63 Marks

A card is drawn at random from a well-shuffled pack of 52 playing cards. Complete the following activity to find the probability of the events that the card drawn is (i) a heart (ii) not a face card. The sample space S contains 52 sample points.
$\therefore n(S)=52$.
(i) Let A be the event of getting a heart card.
There are ⬜ cards of heart. $\quad$$\quad$∴n(A) = ⬜
$P(A)=\frac{n(A)}{n(S)}$
$\therefore P(A)$= $[-]$
(ii) Let B be the event of not getting a face card.
There are ⬜ cards which are not face cards.$\quad$$\quad$∴n(B) = ⬜
$P(B)=\frac{n(B)}{n(S)}$
$\therefore P(B)$= $[-]$

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Maths 3 Marks Question

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