# Solved Probability Problems

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 step-by-step 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 (viii) The card is black (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.

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