[2 Mark Question Answer]

Question 12 Marks

Two coins are tossed together. Find the probability of getting: at most one head

Answer

Total outcomes $= 4$
i.e., $\text{HH, HT, TT, TH}$
Favourable outcomes $=3$
i.e., $\text{HH , HT}$ and $\text{TH}$
$P(E)=\frac{3}{4}$

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Question 22 Marks

Two coins are tossed together. Find the probability of getting: no head

Answer

Total outcomes $=4$
i.e.,$\text{ HH, HT, TT, TH}$
Favourable outcomes $=1$
i.e., $\text{TT}$
$P(E)=\frac{1}{4}$

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Question 32 Marks

Two coins are tossed together. Find the probability of getting: at least one head

Answer

Total outcomes $=4$
i.e.,$\text{ HH, HT, TT, TH}$
Favourable outcomes $=3$
i.e., $\text{HH}$ and $\text{HT & TH}$
$P(E)=\frac{3}{4}$

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Question 42 Marks

Two coins are tossed together. Find the probability of getting: exactly one tail

Answer

Total outcomes $= 4$
i.e., $\text{HH, HT, TT, TH}$
Favourable outcomes $=2$ i.e., $\text{HT}$ and $\text{TH}$
$P ( E )=\frac{2}{4}=\frac{1}{2}$

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Question 52 Marks

A die is thrown once. Find the probability of getting:a number greater than $6$.

Answer

Total outcomes $=6$ i.e., $1,2,3,4,5$ and $6$
Favourable outcomes $=0$
$P(E)=\frac{0}{6}=0$

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Question 62 Marks

A die is thrown once. Find the probability of getting:a number less than $6$

Answer

Total outcomes $=6$ i.e., $1,2,3,4,5$ and $6$
Favourable outcomes $=5$
i.e. $1,2,3,4$, and $5$
$P(E)=\frac{5}{6}$

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Question 72 Marks

A die is thrown once. Find the probability of getting:a number other than $3$ and $5$

Answer

Total outcomes $=6$
$\text { i.e., } 1,2,3,4,5 \text { and } 6$
Favourable outcomes $=4$
i.e. $1,2,4,6$
$P(E)=\frac{4}{6}=\frac{2}{3}$

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Question 82 Marks

A die is thrown once. Find the probability of getting:a number greater than $3$

Answer

Total outcomes $=6$
i.e., $1,2,3,4,5$ and $6$
Favourable outcomes $=3$
i.e. $4,5,6$
$P(E)=\frac{3}{6}=\frac{1}{2}$

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Question 92 Marks

A die is thrown once. Find the probability of getting$:$a prime number

Answer

Total outcomes $=6$ i.e., $1,2,3,4,5$ and $6$
Favourable outcomes $=3$
i.e. $2,3,5$
$P(E)=\frac{3}{6}=\frac{1}{2}$

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Question 102 Marks

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is: less than or equal to $12$

Answer

Total outcomes $= 36$ i.e.
$ (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)$
$ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)$
Favourable outcomes $= 36$
$ \text { P(E) = } \frac{36}{36}=1$

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Question 112 Marks

From $10$ identical cards, numbered $1, 2, 3, ……, 10$, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of $2$ and $3$

Answer

Total outcomes $=10$
i.e. $1,2,3,4,5,6,7,8,9,10$
Favourable outcomes $=1$
i.e. $6$
$P(E)=\frac{1}{10}$

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Question 122 Marks

From $10$ identical cards, numbered $1, 2, 3, ……, 10$, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of $3$

Answer

Total outcomes $=10$
i.e. $1,2,3,4,5,6,7,8,9,10$
Favourable outcomes $=3$
i.e. $3,6,9$
$P(E)=\frac{3}{10}$

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Question 132 Marks

Three identical coins are tossed together. What is the probability of obtaining: no head?

Answer

Total outcomes $=8$
i.e. $\text{(H, H, H),(H, H, T),(H, T, H),(T, T, T),(T, H, H),(T, T, H),(H, T, T),(T, H, T)}$
Favourable outcome $=1$ i.e. $\text{( T , T , T )}$
$\therefore P(E)=\frac{1}{8}$

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Question 142 Marks

Three identical coins are tossed together. What is the probability of obtaining: exactly one head?

Answer

Total outcomes $=8$
i.e. $\text{(H, H, H),(H, H, T),(H, T, H),(T, T, T),(T, H, H),(T, T, H),(H, T, T),(T, H, T)}$
Favourable outcome $=3\text{( H , T , H ),( T , T , H ),( H , T , T )}$
$\therefore P(E)=\frac{3}{8}$

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Question 152 Marks

Three identical coins are tossed together. What is the probability of obtaining: exactly two heads?

Answer

Total outcomes $=8$
i.e. $\text{( H , H , H ),( H , H , T ),( H , T , H ),( T , T , T ),( T , H , H ),( T , T , H ),( H , T , T ),( T , H , T )}$
Favourable outcome $=3\text{( H , H , T ),( H , T , H ),( T , H , H )}$
$\therefore P(E)=\frac{3}{8}$

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Question 162 Marks

Three identical coins are tossed together. What is the probability of obtaining: all heads?

Answer

Total outcomes $=8$
i.e. $\text{(H, H, H),(H, H, T),(H, T, H),(T, T, T),(T, H, H),(T, T, H),(H, T, T),(T, H, T)}$
Favourable outcome = i.e. $\text{( H , H , H )}$
$\therefore P \left(\right.$ of getting all heads$)$ $=\frac{1}{8} C$

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Question 172 Marks

Which of the following can not be the probability of an event?
$\text { (i) } \frac{2}{7}$ $(ii) 3.8$ $(iii) 37 \%$ $(iv) -0.8$ $(v) 0.8$ $(vi) \frac{-2}{5}$ $(vii) \frac{7}{8}$

Answer

The probability of an event cannot be
$(ii) 3.8$ i.e. the probability of an event cannot exceed $1$.
$(iv) i.e. -0.8$ and
$(vi) -2/5$, This is because the probability of an event can never be less than $1$.

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