Basic Probability Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Two dice are rolled. The probability that the sum is 8 is
ExplanationFavourable: (2,6), (3,5), (4,4), (5,3), (6,2) = 5 out of 36.
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Question 2 of 50
Two coins are tossed. The probability of getting two heads is
ExplanationSample space: HH, HT, TH, TT; one favourable outcome out of 4.
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Question 3 of 50
The probability of a sure (certain) event is
ExplanationA certain event always happens, so its probability is 1.
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Question 4 of 50
Two dice are rolled. The probability that the sum is 7 is
ExplanationFavourable: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 out of 36 = 1/6.
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Question 5 of 50
For the same independent events, P(A) = 1/2 and P(B) = 1/3, P(A or B) is
ExplanationP(A or B) = 1/2 + 1/3 - 1/6 = 2/3.
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Question 6 of 50
The number of possible outcomes when three coins are tossed is
Explanation2 x 2 x 2 = 8.
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Question 7 of 50
The probability of getting a 4 when a fair die is rolled is
ExplanationOne favourable outcome out of 6.
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Question 8 of 50
The probability of getting a number greater than 4 when a die is rolled is
ExplanationFavourable outcomes: 5 and 6, so P = 2/6 = 1/3.
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Question 9 of 50
The probability of drawing a heart or an ace from a deck is
Explanation13 + 4 - 1 (ace of hearts counted twice) = 16, so P = 16/52 = 4/13.
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Question 10 of 50
The probability of drawing the queen of hearts from a standard deck is
ExplanationThere is only one queen of hearts.
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Question 11 of 50
Two dice are rolled. The probability that the sum is less than 4 is
ExplanationSum 2: (1,1); sum 3: (1,2), (2,1). That is 3 out of 36 = 1/12.
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Question 12 of 50
The probability of drawing a card that is neither a heart nor an ace is
Explanation1 - 4/13 = 9/13.
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Question 13 of 50
If the probability of rain tomorrow is 0.3, the probability of no rain is
ExplanationP(not A) = 1 - P(A) = 1 - 0.3 = 0.7.
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Question 14 of 50
If the probability of winning a game is 2/5, the odds in favour of winning are
ExplanationOdds in favour = P(win) : P(lose) = 2/5 : 3/5 = 2 : 3.
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Question 15 of 50
A coin is tossed and a die is rolled. The probability of getting a head and a 6 is
ExplanationIndependent events: 1/2 x 1/6 = 1/12.
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Question 16 of 50
The probability of drawing an ace from a standard deck of 52 cards is
ExplanationThere are 4 aces, so P = 4/52 = 1/13.
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Question 17 of 50
Two dice are rolled. The probability that the sum is greater than 9 is
ExplanationSums 10 (3 ways), 11 (2), 12 (1) = 6 ways, so P = 6/36 = 1/6.
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Question 18 of 50
Two dice are rolled. The probability that the sum is 12 is
ExplanationOnly (6,6) gives 12, so P = 1/36.
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Question 19 of 50
Two dice are rolled. The probability that the sum is a prime number is
ExplanationPrime sums: 2 (1 way), 3 (2), 5 (4), 7 (6), 11 (2) = 15 ways, so P = 15/36 = 5/12.
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Question 20 of 50
The probability of drawing a red king from a deck is
ExplanationThere are 2 red kings (hearts and diamonds), so P = 2/52 = 1/26.
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Question 21 of 50
The probability of getting a head when a fair coin is tossed is
ExplanationThere are 2 equally likely outcomes, H and T, so P(H) = 1/2.
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Question 22 of 50
The probability of drawing a heart from a standard deck of 52 cards is
ExplanationThere are 13 hearts, so P = 13/52 = 1/4.
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Question 23 of 50
The probability of drawing a king or a queen from a deck of 52 cards is
ExplanationThese events cannot both occur, so P = 4/52 + 4/52 = 8/52 = 2/13.
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Question 24 of 50
The probability of getting 7 when a single die is rolled is
ExplanationA die has no face showing 7, so the event is impossible.
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Question 25 of 50
The probability of an impossible event is
ExplanationAn impossible event never happens, so its probability is 0.
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Question 26 of 50
Two coins are tossed. The probability of getting exactly one head is
ExplanationFavourable outcomes: HT and TH, so P = 2/4 = 1/2.
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Question 27 of 50
The probability of NOT drawing an ace from a deck is
ExplanationP(not ace) = 1 - 4/52 = 12/13.
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Question 28 of 50
A and B are independent events with P(A) = 1/2 and P(B) = 1/3. P(A and B) is
ExplanationFor independent events P(A and B) = P(A) x P(B) = 1/6.
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Question 29 of 50
A fair die is rolled 60 times. The expected number of sixes is
ExplanationExpected number = n x p = 60 x 1/6 = 10.
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Question 30 of 50
A card is drawn and it is known to be red. The probability that it is a king is
ExplanationOf the 26 red cards, 2 are kings, so P = 2/26 = 1/13.
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Question 31 of 50
Three coins are tossed. The probability of getting exactly two heads is
ExplanationFavourable outcomes: HHT, HTH, THH = 3 out of 8.
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Question 32 of 50
Two cards are drawn one after another without replacement. The probability that both are aces is
Explanation4/52 x 3/51 = 12/2652 = 1/221.
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Question 33 of 50
Two cards are drawn one after another with replacement. The probability that both are hearts is
ExplanationIndependent events: 1/4 x 1/4 = 1/16.
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Question 34 of 50
Three coins are tossed. The probability of getting all heads is
ExplanationOne favourable outcome (HHH) out of 8.
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Question 35 of 50
The probability of getting a number less than 3 when a die is rolled is
ExplanationFavourable outcomes: 1 and 2, so P = 2/6 = 1/3.
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Question 36 of 50
Two dice are rolled. The probability of getting a doublet (same number on both) is
ExplanationDoublets: (1,1) to (6,6) = 6 outcomes, so P = 6/36 = 1/6.
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Question 37 of 50
The number of possible outcomes when two dice are rolled together is
Explanation6 x 6 = 36.
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Question 38 of 50
The probability of getting an even number when a die is rolled is
ExplanationFavourable outcomes: 2, 4, 6, so P = 3/6 = 1/2.
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Question 39 of 50
A fair coin is tossed three times. The probability of getting at least one head is
ExplanationP(at least one head) = 1 - P(no head) = 1 - 1/8 = 7/8.
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Question 40 of 50
The number of possible outcomes when a die is rolled once is
ExplanationThe sample space is {1, 2, 3, 4, 5, 6}.
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Question 41 of 50
A bag contains 3 red and 2 blue balls. The probability of drawing a red ball is
ExplanationP = favourable / total = 3/5.
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Question 42 of 50
A bag has 4 red, 3 green and 5 blue balls. The probability of drawing a ball that is not blue is
ExplanationNot blue = 4 + 3 = 7 balls out of 12.
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Question 43 of 50
The probability of drawing a face card (jack, queen or king) from a deck is
ExplanationThere are 12 face cards, so P = 12/52 = 3/13.
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Question 44 of 50
The probability of getting a prime number when a die is rolled is
ExplanationPrimes on a die: 2, 3, 5, so P = 3/6 = 1/2.
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Question 45 of 50
A bag has 5 red and 3 blue balls. Two balls are drawn without replacement. The probability that both are red is
Explanation5/8 x 4/7 = 20/56 = 5/14.
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Question 46 of 50
Two dice are rolled. The probability of getting at least one 6 is
ExplanationP = 1 - P(no 6) = 1 - 25/36 = 11/36.
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Question 47 of 50
Two dice are rolled. The probability that the first shows 3 and the second shows more than 4 is
Explanation1/6 x 2/6 = 1/18.
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Question 48 of 50
Two coins are tossed. The probability of getting at least one head is
ExplanationOutcomes with at least one head: HH, HT, TH = 3 out of 4.
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Question 49 of 50
The probability of drawing a red card from a standard deck of 52 cards is
ExplanationThere are 26 red cards (hearts and diamonds).
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Question 50 of 50
Two dice are rolled. The probability that the product of the numbers is 6 is
ExplanationFavourable: (1,6), (6,1), (2,3), (3,2) = 4 out of 36 = 1/9.
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