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1Exercise 16.1
A coin is tossed three times. Find the probability of getting exactly two heads.
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Total outcomes: 2³ = 8.
Exactly two heads: HHT, HTH, THH → 3 favourable.
P = 3/8
2Exercise 16.1
Two dice are thrown. Find the probability that the sum of the numbers on the dice is 7.
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Total outcomes = 36.
Favourable (sum 7): (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6.
P = 6/36 = 1/6
3Exercise 16.1
A card is drawn from a well-shuffled deck of 52 cards. Find the probability that it is (i) an ace, (ii) a black card.
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(i) Aces: 4. P = 4/52 = 1/13
(ii) Black cards: 26. P = 26/52 = 1/2
4Exercise 16.1
If P(A) = 0.6, P(B) = 0.3 and P(A∩B) = 0.2, find P(A∪B).
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P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.6 + 0.3 - 0.2
= 0.7
5Exercise 16.1
A bag contains 4 red and 6 black balls. Two balls are drawn at random. Find the probability that both are red.
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Total balls = 10.
Total ways = 10C2 = 45.
Favourable (both red) = 4C2 = 6.
P = 6/45 = 2/15
6Exercise 16.1
If P(A) = 1/2, P(B) = 1/3 and P(A∩B) = 1/6, are A and B independent events?
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For independence: P(A∩B) = P(A)·P(B)
P(A)·P(B) = (1/2)(1/3) = 1/6 = P(A∩B)
Yes, A and B are independent events.