Solve The Following Question.1MARKS

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

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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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Maths Solve The Following Question.1MARKS

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