17. From a pack of cards one card is drawn randomly. Find the probability of its being a
diamond, heart or club?
18. Find the probability of a non-leap year having 53 Sundays.
19. A leap year is selected randomly. Find the probability of this year having 52
Sundays.
Answers
Answer:
17.
→ From a pack of cards, one card is drawn randomly.
∴ n (S) = 52
Let 'A' be the event where the card drawn is diamond, heart or club :-
A = { DIAMOND : Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King, HEART : Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King,
CLUB : Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King. }
∴ n (A) = 39
∴ Probability of (A) = n (A)/ n (S)
= 39/ 52
= 3/4
∴ The probability of the card being Heart, Diamond or Club is 3/4.
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18.
→ A non-leap year has 365 days.
∴ n (S) = 365
In 365 days,
Number of weeks = 52 weeks and 1 day is remaining.
For 52 weeks number of Sundays = 52
∴ 1 remaining day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
∴ n (A) = 1
∴ n (S) = 7
∴ p (A) = n (A) / n (S)
= 1/7
∴ The probability of a non leap year having 53 is 1/7.
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19.
→ A leap year has 366 days.
i.e, it has 52 complete weeks (including Sundays) and 2 extra days.
∴ n (S) = 7
It is these 2 days where there are no Sundays.
Let 'B' be the event of favourable outcomes.
∴ It is evident that from cases (1) to (5) there will be no Sunday in them so there are 5 cases favourable to the event.
∴ n (B) = 5
∴ p (A) = n (A) / n (S)
= 5/7
∴ The probability of this year having 52 Sundays is 5/7.
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