**Solved Probability Problems for Grade 11 :**

Here we are going to see some example problems on probability.

Let S be the sample space associated with a random experiment and A be an event. Let n(S) and n(A) be the number of elements of S and A respectively. Then the probability of the event A is defined as

P(A) = n(A)/n(S)

= Number of cases favourable to A/Exhaustive number of cases in S

**Question 1 :**

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

**Solution :**

Sample space = {1, 2, 3, 4, ...........100}

n (S) = 100

Let "A" be the event of choosing a number is a prime

A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

n(A) = 25

P(A) = n(A)/n(S) = 25/100

Let "B" be the event of choosing be a multiple of 8.

B = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}

n(A) = 12

P(B) = n(B)/n(S) = 12/100

P(A or B) = P(A) + P(B)

= 25/100 + 12/100

= 37 /100

**Question 2 :**

A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that (i) all are red (ii) one red and 2 black.

**Solution :**

Total number of balls = 7 red + 4 black

= 11 balls

n(S) = ^{11}C_{3}

= (11⋅10⋅9)/(3⋅2⋅1)

= 165

Let "A" be the event of getting 3 balls are in red color.

n(A) = ^{7}C_{3}

= (7⋅6⋅5)/(3⋅2⋅1)

= 35

P(A) = n(A)/n(S)

= 35/165

P(A) = 7/33

(ii) one red and 2 black.

Let "B" be the event of getting 1 red and 2 black balls.

n(B) = ^{7}C_{1 }⋅ ^{4}C_{2}

= 7 ⋅ 6

= 42

P(B) = n(B)/n(S)

= 42/165

P(B) = 14/55

**Question 3 :**

A single card is drawn from a pack of 52 cards. What is the probability that (i) the card is an ace or a king (ii) the card will be 6 or smaller (iii) the card is either a queen or 9?

Solution :

Number of cards = 52

n(S) = 52

(i) the card is an ace or a king

Let "A" and "B" be the events of getting an ace and king card respectively.

n(A) = 4 ==> P(A) = n(A) / n(S) = 4/52

n(B) = 4 ==> P(B) = n(B) / n(S) = 4/52

P(A or B) = P(A) + P(B)

= (4/52) + (4/52)

= 8/52

P(A or B) = 2/13

(ii) the card will be 6 or smaller

Let "C" and "D" be the events of getting 6 and smaller than 6 respectively.

Out of 13 spade cards, there will be 1 card numbered 6.

Out of 13 diamond cards, there will be 1 card numbered 6.

Out of 13 clever cards, there will be 1 card numbered 6.

Out of 13 heart cards, there will be 1 card numbered 6.

So, there are 4 cards numbered 6.

n(C) = 4 ==> P(C) = n(C) / n(S) = 4/52

There will be 5 cards in each set of cards.

n(D) = 16 ==> P(D) = n(D) / n(S) = 16/52

P(C or D) = P(C) + P(D)

= (4/52) + (16/52)

= 20/52

P(C or D) = 5/13

(iii) the card is either a queen or 9?

Let "E" and "F" be the events of getting queen and a card numbered 9 respectively.

There will be 4 queen cards in 52 cards.

n(E) = 4 ==> p(E) = n(E)/n(S) = 4/52

n(F) = 4 ==> p(F) = n(F)/n(S) = 4/52

P(C or D) = P(C) + P(D)

= (4/52) + (4/52)

= 8/52

P(E or F) = 2/13

After having gone through the stuff given above, we hope that the students would have understood, "Solved Probability Problems for Grade 11"

Apart from the stuff given in "Solved Probability Problems for Grade 11", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**