1 Marks Question

Question 11 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a ten.

Answer

Since there are four $10s,$ the probability is: $=\frac{4}{52} =\frac{ 1}{13}$

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Question 21 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a black card.

Answer

Since there are $26$ black cards, the probability is: $=\frac{26}{52} = \frac{1}{2}$

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Question 31 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:a queen.

Answer

Since there are $4$ queens, the probability is: $=\frac{4}{52} = \frac{1}{13}$

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Question 41 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: the ace of spades.

Answer

There is only $1$ card named ace of spade. Hence, the probability is $=\frac{1}{52}$

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Question 51 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a jack, queen or a king.

Answer

There are $4$ jacks, $4$ queens and $4$ kings in a deck. Hence, the probability of drawing either of them is: $=\frac{(4+4+4)}{52} = \frac{3}{13}$

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Question 61 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: neither a heart nor a king.

Answer

This means that we have to leave the hearts and the kings out. There are $13$ hearts and $3$ kings (other than that of hearts). Hence, the probability of drawing neither a heart nor a king is: $=\frac{(52-13-3)}{52} = \frac{9}{13}$

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Question 71 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: spade or an ace.

Answer

There are $13$ spades and $3$ aces (other than that of spades). Hence the probability is: $=\frac{(13+3)}{52} = \frac{4}{13}$

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Question 81 Mark

When two dice are rolled: List the outcomes for the event that total is less than $5.$

Answer

Possible outcomes when two dice are rolled: $S = \{(1, 1), (1, 2), (1, 3), (1, 4),$ _____, $(6, 5), (6, 6)\}$ Therefore, the number of possible outcomes in the sample space is $36.$ The outcomes for the event that total is less than $5:B = \{(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)\}$

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Question 91 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: neither an ace nor a king.

Answer

This means that we have to leave the aces and the kings out. There are $4$ aces and $4$ kings. Hence, the probability of drawing neither an ace nor a king is: $=\frac{(52-4-4)}{52} = \frac{11}{13}$

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Question 101 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: black and a king.

Answer

This question is exactly the same as part $(i).$ Hence, the probability is: $=\frac{2}{52} = \frac{1}{26}$

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Question 111 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a red card.

Answer

Since there are $26$ red cards, the probability is $=\frac{26}{52} = \frac{1}{2}$

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Question 121 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a black king.

Answer

There are two black kings, spade and clover. Hence, the probability that the drawn card is a black king is: $=\frac{2}{52} = \frac{1}{26}$

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Question 131 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a spade.

Answer

Since there are $13$ spades, the probability is: $=\frac{13}{52} = \frac{1}{4}$

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Question 141 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: jack.

Answer

Since there are $4$ jacks, the probability is: $=\frac{4}{52} =\frac{ 1}{13}$

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Question 151 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: a heart.

Answer

Since there are $13$ hearts, the probability is: $=\frac{13}{52} = \frac{1}{4}$

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Question 161 Mark

When two dice are rolled: Find probability of getting an odd total.

Answer

Possible outcomes when two dice are rolled: $S = \{(1, 1), (1, 2), (1, 3), (1, 4),$ _____$, (6, 5), (6, 6)\}$ Therefore, the number of possible outcomes in the sample space is $36.$ The number of favourable outcomes is $18.$
$\therefore\text{ P(E)}=\frac{18}{36}=\frac{1}{2}$

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Question 171 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: either a black card or a king.

Answer

There are $26$ black cards and $4$ kings, but two kings are already black.
Hence, we only need to count the red kings.
Thus, the probability is $=\frac{(26+2)}{52} = \frac{7}{13}$

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Question 181 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: other than an ace.

Answer

It means that we have to leave out the aces. Since there are $4$ aces, then the probability is $=\frac{(52-4)}{52} = \frac{12}{13}$

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Question 191 Mark

When two dice are rolled:
Find the probability of getting a total less than $5?$

Answer

Possible outcomes when two dice are rolled:
$S = \{(1, 1), (1, 2), (1, 3), (1, 4),$ _____$, (6, 5), (6, 6)\}$
Therefore, the number of possible outcomes in the sample space is $36.$
The number of favourable outcomes is $6.$
$\therefore \text{P(B)}=\frac{6}{36}=\frac{1}{6}$

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Question 201 Mark

When two dice are rolled: List the outcomes for the event that the total is odd.

Answer

Possible outcomes when two dice are rolled: $S = \{(1, 1), (1, 2), (1, 3), (1, 4),$ _____$, (6, 5), (6, 6)\}$
Therefore, the number of possible outcomes in the sample space is $36.$ The outcomes for the event that the total is odd: $E = \{(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1),$ $(6, 3), (6, 5)$

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Question 211 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is: the seven of clubs

Answer

There is only one card named seven of clubs. Hence, the probability is $=\frac{1}{52}$

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Question 221 Mark

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
neither a red card nor a queen.

Answer

This means that we have to leave the red cards and the queens out. There are $26 $ red cards and $2$ queens (only black queens are counted since the reds are already counted among the red cards). Hence, the probability of drawing neither a red card nor a queen is:
$=\frac{(52-26-2)}{52} =\frac{ 6}{13}$

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