Solved probability problems and solutions are given here for a concept with clear understanding.
Students can get a fair idea on the probability questions which are provided with the detailed stepbystep answers to every question.
Solved probability problems with solutions:
1.
The graphic above shows a container with 4 blue triangles, 5 green squares and 7 red circles. A single object is drawn at random from the container.
Match the following events with the corresponding probabilities:
(i) The objects is not a circle (ii) The objects is a triangle (iii) The objects is not a triangle (iv) The objects is not a square (v) The objects is a circle (vi) The objects is a square 
(a) 5/16 (b) 4/16 (c) 7/16 (d) 9/16 (e) 12/16 (f) 11/16 
Solution:
Number of blue triangles in a container = 4
Number of green squares = 5
Number of red circles = 7
Total number of objects = 4 + 5 + 7 = 16
(i) The objects is not a circle:
P(the object is a circle)
= Number of circles/Total number of objects
= 7/16
P(the object is not a circle)
= 1  P(the object is a circle)
= 1  7/16
= (16  7)/16
= 9/16
(ii) The objects is a triangle:
P(the object is a triangle)
= Number of triangle/Total number of objects
= 4/16
(iii) The objects is not a triangle:
P(the object is a triangle)
= Number of triangles/Total number of objects
= 4/16
P(the object is not a triangle)
= 1  P(the object is a triangle)
= 1  4/16
= (16  4)/16
= 12/16
(iv) The objects is not a square:
P(the object is a square)
= Number of squares/Total number of objects
= 5/16
P(the object is not a square)
= 1  P(the object is a square)
= 1  5/16
= (16  5)/16
= 11/16
(v) The objects is a circle:
P(the object is a circle)
= Number of circles/Total number of objects
= 7/16
(vi) The objects is a square:
P(the object is a square)
= Number of squares/Total number of objects
= 5/16
Match the following events with the corresponding probabilities are shown below:
(i) The objects is not a circle (ii) The objects is a triangle (iii) The objects is not a triangle (iv) The objects is not a square (v) The objects is a circle (vi) The objects is a square 
(d) 9/16 (b) 4/16 (e) 12/16 (f) 11/16 (c) 7/16 (a) 5/16 
2. A single card is drawn at random from a standard deck of 52 playing cards.
Match each event with its probability.
Note: fractional probabilities have been reduced to lowest terms. Consider the ace as the highest card.
(i) The card is a diamond (ii) The card is a red
king (iii) The card is a king or queen (iv) The card is either a red or an ace (v) The card is not a king (vi) The card is a five or lower (vii) The card is a king (viii) The card is black 
(a) 1/2 (b) 1/13 (c) 1/26 (d) 12/13 (e) 2/13 (f) 1/4 (g) 4/13 (h) 7/13 
Solution:
Total number of playing cards = 52
(i) The card is a diamond:
Number of diamonds in a deck of 52 cards = 13
P(the card is a diamond)
= Number of diamonds/Total number of playing cards
= 13/52
= 1/4
(ii) The card is a red king:
Number of red king in a deck of 52 cards = 2
P(the card is a red king)
= Number of red kings/Total number of playing cards
= 2/52
= 1/26
(iii) The card is a king or queen:
Number of kings in a deck of 52 cards = 4
Number of queens in a deck of 52 cards = 4
Total number of king or queen in a deck of 52 cards = 4 + 4 = 8
P(the card is a king or queen)
= Number of king or queen/Total number of playing cards
= 8/52
= 2/13
(iv) The card is either a red card or an ace:
Total number of red card or an ace in a deck of 52 cards = 28
P(the card is either a red card or an ace)
= Number of cards which is either a red card or an ace/Total number of playing cards
= 28/52
= 7/13
(v) The card is not a king:
Number of kings in a deck of 52 cards = 4
P(the card is a king)
= Number of kings/Total number of playing cards
= 4/52
= 1/13
P(the card is not a king)
= 1  P(the card is a king)
= 1  1/13
= (13  1)/13
= 12/13
(vi) The card is a five or lower:
Number of cards is a five or lower = 16
P(the card is a five or lower)
= Number of card is a five or lower/Total number of playing cards
= 16/52
= 4/13
(vii) The card is a king:
Number of kings in a deck of 52 cards = 4
P(the card is a king)
= Number of kings/Total number of playing cards
= 4/52
= 1/13
(viii) The card is black:
Number of black cards in a deck of 52 cards = 26
P(the card is black)
= Number of black cards/Total number of playing cards
= 26/52
= 1/2
Match the following events with the corresponding probabilities are shown below:
(i) The card is a diamond (ii) The card is a red
king
(iii) The card is a king or queen (iv) The card is either a red or an ace (v) The card is not a king (vi) The card is a five or lower (vii) The card is a king 
(f) 1/4 (c) 1/26 (e) 2/13 (h) 7/13
(d) 12/13 (g) 4/13 (b) 1/13 (a) 1/2 
The examples can help the students to practice more questions on probability by following the concept provided in the solved probability problems.
`Probability
Probability of Tossing Two Coins
Probability of Tossing Three Coins
Probability for Rolling Two Dice
Probability for Rolling Three Dice
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