Page 351 - Start Up Mathematics_8 (Non CCE)

Solution: Total number of outcomes when two dice are rolled simultaneously = 36 (i.e., 6 × 6)
(a) Let A be the event of getting the sum as an odd number, i.e., 3, 5, 7, 9 and 11.

The outcomes favourable to event A are (1, 2), (2, 1), (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 5),
(3, 4), (4, 3), (5, 2), (6, 1), (3, 6), (4, 5), (5, 4), (6, 3), (5, 6) and (6, 5).

\ Favourable outcomes =18
Favourable outcomes 18 1
Hence, P(A) = = =
Total outcomes 36 2
(b) Let B be the event of getting a doublet.
The outcomes favourable to B are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
\ Favourable outcomes = 6
Favourable outcomes 6 1
Hence, P(B) = = =
Total outcomes 36 6
(c) Let D be the event of getting a multiple of 2 on one die and a multiple of 3 on the other, i.e.,
2, 3, 4 and 6.
The outcomes favourable to event D are (2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2),
(3, 4), (3, 6), (6, 2) and (6, 4).
\ Favourable outcomes = 11

Favourable outcomes 11
Hence, P(D) = =
Total outcomes 36
(d) Let E be the event of getting a total of at least 11, i.e., 11 and 12.
The outcomes favourable to event E are (5, 6), (6, 5) and (6, 6).
\ Favourable outcomes = 3
Favourable outcomes 3 1
Hence, P(E) = = =
Total outcomes 36 12

Example 6: A card is drawn from a well-shuffled deck of 52 cards, find the probability of:
(a) getting a club card. (b) getting a red card. (c) getting a black queen.
Solution: A deck of playing cards has 52 cards.
\ Total number of outcomes = 52

(a) Let A be the event of getting a club card. There are 13 club cards.
\ Favourable outcomes = 13
Favourable outcomes 13 1
Hence, P(A) = = =
Total numberof outcomes 52 4
(b) Let B be the event of getting a red card. There are 26 red cards in a deck of playing cards.

\ Favourable outcomes = 26
Favourable outcomes 26 1
Hence, P(B) = = =
Total outcomes 52 2
(c) Let C be the event of getting a black queen. There are 2 black queens.

\ Favourable outcomes = 2
Favourable outcomes 2 1
Hence, P(C) = = =
Total outcomes 52 26

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