[2 Mark Question Answer]

Question 12 Marks

A coin is tossed once. What is the probability of getting a tail?

Answer

When a coin is tossed once, the possible outcomes are H and T.
Total number of possible outcomes = 2
Favourable outcome = 1
∴ Probability of getting a tail = P (T)
$=\frac{\text { Number of favourable outcomes }}{\text { Total number of possible outcomes }}=\frac{1}{2}$

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Question 22 Marks

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is An even-numbered red card?

Answer

No. of total cards = 52
cards removed of 4 colours of multiples of 3
= 3, 6, 9 = 4 x 3 = 12
Remaining cards = 52 - 12 = 40
An even number red cards = 2, 4, 8, 10 card = 2 x 4 = 8
⇒ Probability P(E) = $\frac{8}{40}=\frac{1}{5}$

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Question 32 Marks

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is A face card (King, Jack or Queen).

Answer

No. of total cards = 52
cards removed of 4 colours of multiples of 3
=3, 6, 9 = 4 x 3 =12
Remaining cards = 52 - 12 = 40
No.of face cards =12 cards
⇒ Probability p(E) = $\frac{12}{40}=\frac{3}{10}$

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Question 42 Marks

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

Answer

n(S) = 52.
Event = {getting neither a red card nor a queen}
∴ There are 26 red cards and 2 more queens are there.
Number of cards each one of which is either a red card or a queen = 28.
The event that the card drawn is neither a red card nor a queen = 52 - 28 = 24.
n(E) = 24
n(S) = 52
P(E) = ?
∴ P(E) = $\frac{ n ( E )}{ n ( S )}=\frac{24}{52}=\frac{6}{13}$

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Question 52 Marks

1800 families with 2 children were selected randomly and the following data were recorded:

No. of girls in a family	2	1	0
No. of families	700	850	250

Computer the probability of a family chosen at random having: 1 girl.

Answer

Total number of families
n(S) = 1800
Event = { 1 girl }
n(E) = 850
P(E) = ?
P(E) = $\frac{ n ( E )}{ n ( S )}=\frac{850}{1800}=\frac{17}{36}$

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Mathematics [2 Mark Question Answer]

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