Answer:
(a) P(nine or seven or jack) = 3/13
(b) P(heart or spade or club) = 3/4
(c) P(queen or two or spade) = 21/52
(d) P(nine or ten or diamond or heart) = 17/26
Step-by-step explanation:
(a) In a deck of 52 cards, there are 4 nines, 4 sevens and 4 jacks.
Probability of picking a nine = P(nine) = 4/52 = 1/13
Probability of picking a seven = P(seven) = 4/52 = 1/13
Probability of picking a jack = P(jack) = 4/52 = 1/13
∴ P(nine or seven or jack) = P(nine) + P(seven) + P(jack) = 1/13 + 1/13 + 1/13 = 3/13
∴ P(nine or seven or jack) = 3/13
(b) In a deck of 52 cards, there are 13 hearts, 13 spades and 13 clubs.
Probability of picking a heart = P(heart) = 13/52 = 1/4
Probability of picking a spade = P(spade) = 13/52 = 1/4
Probability of picking a club = P(club) = 13/52 = 1/4
∴ P(heart or spade or club) = P(heart) + P(spade) + P(club) = 1/4 + 1/4 + 1/4 = 3/4
∴ P(heart or spade or club) = 3/4
(c) In a deck of 52 cards, there are 4 queens, 4 twos and 13 spades.
Probability of picking a queen = P(queen) = 4/52 = 1/13
Probability of picking a two = P(two) = 4/52 = 1/13
Probability of picking a spade = P(spade) = 13/52 = 1/4
∴ P(queen or two or spade) = P(queen) + P(two) + P(spade) = 1/13 + 1/13 + 1/4 = 21/52
∴ P(queen or two or spade) = 21/52
(d) in a deck of 52 cards, there are 4 nines, 4 tens, 13 diamonds and 13 hearts.
Probability of picking a nine = P(nine) = 4/52 = 1/13
Probability of picking a ten = P(ten) = 4/52 = 1/13
Probability of picking a diamond = P(diamond) = 13/52 = 1/4
Probability of picking a heart = P(heart) = 13/52 = 1/4
∴ P(nine or ten or diamond or heart) = P(nine) + P(ten) + P(diamond) + P(heart) = 1/13 + 1/13 + 1/4 + 1/4 = 17/26
∴ P(nine or ten or diamond or heart) = 17/26
