**Probability Word Problems for Grade 10 :**

Here we are going to see, some word problems on probability.

**Question 1 :**

If two dice are rolled, then find the probability of getting the product of face value 6 or the difference of face values 5.

**Solution :**

Sample space = {(1, 1) (1, 2) (1, 3) .........(6, 6)}

Let "A" be the even of getting the product of face value 6.

A = {(1, 6)(2, 3)(3, 2)(6, 1)}

n(A) = 4

P(A) = n(A)/n(S) = 4/36

Let "B" be the event of getting the difference of face value as 5.

B = {(1, 6)(6, 1)}

n(B) = 2

P(B) = n(B)/n(S) = 2/36

A n B = {(1, 6)(6, 1)}

P(A n B) = 2/36

Let "AUB" be the event of getting the product of face value 6 or the difference of face values 5.

P(A U B) = P(A) + P(B) - P(A n B)

= (4/36) + (2/36) - (2/36)

= 4/36

P(A U B) = 1/9

**Question 2 :**

In a two children family, find the probability that there is at least one girl in a family.

**Solution :**

Sample space = {BB, GG, BG, GB}

n(S) = 4

Let "A" be the event of getting atleast one girl in the family.

A = {GG, BG, GB}

n(A) = 3

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

P(A) = 3/4

**Question 3 :**

A bag contains 5 white and some black balls. If the probability of drawing a black ball from the bag is twice the probability of drawing a white ball then find the number of black balls.

**Solution :**

Let "x" be the number of black balls.

Number of balls = 5(white) + x(black)

n(S) = 5 + x

Let "A" and "B" be the events of getting white and black balls respectively.

P(A) = 5/(5 + x)

P(B) = x/(5 + x)

P(B) = 2P(A)

x/(5+x) = 2(5/(5+x))

x = 10

Hence the number of black balls is 10.

**Question 4 :**

The probability that a student will pass the final examination in both English and Tamil is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Tamil examination?

**Solution :**

Let "A" and "B" be the probabilities of getting pass marks in English and Tamil.

P(A n B) = 0.5

P(A bar n B bar) = 0.1 = P((AUB) whole bar)

P(AUB) = 1 - P((AUB) whole bar)

= 1 - 0.1

P(AUB) = 0.9

P(B) = 0.75

P(A) = ?

P(A n B) = P(A) + P(B) - P(AUB)

0.5 = P(A) + 0.75 - 0.9

0.5 + 0.15 = P(A)

P(A) = 0.65

= 65/100

P(A) = 13/20

**Question 5 :**

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting (i) a diamond (ii) a queen (iii) a spade (iv) a heart card bearing the number 5.

**Solution :**

Here, King, queen and jack of club are removed from the Deck of 52 playing cards.

So remaining cards in deck= 52 - 3 = 49

Total number of outcomes= 49

(i) we know that there are 13 cards of heart.

Let A = event of getting a heart

P(A) = 13/49

(ii)

We know that there are 4 Kings in a deck. After remove removing a king of club we left with 3 kings.

Let B = event of getting a king

Number of favourable outcomes to B = 3

Required probability P(B) = 3/49

(iii)

We know that there are 13 cards of club. After removing king ,queen and jack of club only 10 club cards are left in the deck.

Let C = event of getting a club

Number of favourable outcomes to C = 10

Required probability P(C) = 10/49

After having gone through the stuff given above, we hope that the students would have understood, "Probability Word Problems for Grade 10".

Apart from the stuff given in this section "Probability Word Problems for Grade 10" if you need any other stuff in math, please use our google custom search here.

HTML Comment Box 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**

**Trigonometry 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**

**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**