Experimental Probability

Q.

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

1. True

2. False

3. $\frac{5}{21}$
4. $\frac{7}{21}$

Q.

If two coins are tossed simultaneously, the probability of getting at least one tail is

1. 

2. 

3. 

4. 

Q. Do we really need to convert the fraction into decimal of probability in the exam ?

Q.

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

1. $\frac{11}{18}$

2. $\frac{7}{18}$

3. $\frac{2}{3}$

4. $\frac{5}{18}$

Q. In an experiment, a coin is tossed 1000 times, and every time the tail comes, a die is rolled. It is observed that 6 comes on the die 100 times. Calculate the probability of getting 6 on the die if the probability of getting heads is 0.5.

Q.

1. $\frac{9}{26}$
2. $\frac{3}{26}$
3. None of these
4. $\frac{11}{26}$

Q. A card is drawn from pack of cards. Find the probability of
a) drawing a queen of red colour
b) card drawn having prime number of spade
c) a face card

Q.

Question 6 (i)
A teacher wanted to analyze the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above.So she decided to group them into intervals of varying sizes as follows : 0−20, 20−30…60−70, 70 − 100. Then she formed the following table:
$\begin{array}{cc}\text{Marks}& \text{Number of student}\\ 0-20& 7\\ 20-30& 10\\ 30-40& 10\\ 40-50& 20\\ 50-60& 20\\ 60-70& 15\\ 70-above& 8\\ \text{Total}& 90\end{array}$
(i) Find the probability that a student obtained less than 20% in the mathematics
test.

Q. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:​

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.​

Outcomes	Frequency
3 heads	23
2 heads	72
1 head	77
No head	28

Q. Four coins are tossed simultaneously 810 times with the following frequencies of different outcomes.

No. of heads	4	3	2	1	0
Frequency	150	182	210	129	141

The probability of getting at least 2 tails is

1. $\frac{16}{27}$
2. $\frac{11}{18}$
3. $\frac{2}{3}$
4. $\frac{16}{37}$

Q.

The last page number on the textbooks of different subjects in a class is given.

$\begin{array}{cc}\text{Subject}& \text{Page Number}\\ \text{English}& 203\\ \text{Hindi}& 203\\ \text{Maths}& 152\\ \text{Physics}& 177\\ \text{Chemistry}& 225\\ \text{Biology}& 172\\ \text{Computer Sci.}& 185\\ \text{History}& 203\\ \text{Geography}& 172\\ \text{Moral Sci.}& 267\end{array}$

Find the probability that the last page number ends in
(i) an odd number
(ii) an even number
(iii) a multiple of 3. [4 MARKS]

Q. If the weather prediction of a weather station was correct for 125 days out of 200 days, then find the probability of a wrong prediction on a given day.

1. 0.375
2. 0.735
3. 0.537
4. 0.573

Q. Raj threw a dice 15 times and noted the face-up number each time as given below.
Compute the probability of getting an odd number in the next throw.

1. 0.47
2. 0.53
3. 0.33
4. 0.4

Q.

$20$ cards numbered $1,2,3,...,20$ are put in a box and mixed thoroughly. Shashi draws a card from the box. Find the probability that the number on the card is divisible by $3$

Q.

Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student drawn at random passed the exam?

1. 0.15

2. 0.3

3. 0.35

4. 0.7

Q.

The theoretical probability of getting a head in a toss of a coin is __. Give the answer up to 1 decimal place.

Q.

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

1. $\frac{11}{18}$

2. $\frac{7}{18}$

3. $\frac{2}{3}$

4. $\frac{5}{18}$

Q. A die is rolled 50 times. An even number was obtained 49 times. What is the empirical probability of getting an even number?

1. $\frac{1}{50}$
2. $\frac{49}{50}$
3. $\frac{48}{50}$
4. 1

Q. In a one-day cricket match, a batsman hits the boundary 8 times out of the 48 balls that he faced. Find the probability that he does not hit the boundary.

Q. In a school of 1900 students, there are 800 girls. Find the probability that a student chosen at random is a boy.

1. $\frac{8}{19}$
2. $\frac{11}{27}$
3. $\frac{11}{8}$
4. $\frac{11}{19}$

Q. $O(0,0),A(1,2),B(3,4)$ are the vertices of $△OAB$. The joint equation of the altitude and median drawn from $O$ is

1. $x^2+7xy-y^2=0$
2. $x^2+7xy+y^2=0$
3. $3x^2-xy-2y^2=0$
4. $3x^2+xy-2y^2=0$

Q. the probability for a leap year to have exactly 52 mondays is

Q. Show that $5^0=1$ can be written as ${\log }_{25}1=0$

Q.

In a deck of playing cards, 2 new suits are introduced which are red and black in color respectively. If the number and types of cards in the new suits are same as the standard suits. Find the probability that I will get a face card on a random draw of 1 card. Also find the probability if the new suits were not introduced

1. $\frac{4}{13},\frac{4}{13}$

2. $\frac{3}{13},\frac{3}{13}$

3. $\frac{6}{13},\frac{3}{13}$

4. $\frac{8}{13},\frac{3}{13}$

Q.

In tossing a coin 10 times, the outcomes are

H, H, H, T, H, T, T, T, H, H

The empirical probability of getting a head is (in decimal form)

__

Q. The following table shows the number of times target was hit by a shooter in a shooting game in each of his 10 games.

1	2	4	4	7
3	8	8	9	5

Find the empirical probability that he will exactly hit 8 times in the next game.

1. 0.20
2. 0.40
3. 0.60
4. 0.80

Q. Add the following:

Q. some bags of rice containing the following weights of rice in kg is 4.97, 3.999, 5.05, 5.08, 5.03 , 5.00, 5.04, 4.35, 5.06, 5.00, 5.07, 5.04, 5.00, 4.098, 5.001.find the probability that any of these bags chosen at random contains less than five kg.

Q.

If you throw three coins simultaneously, the probability of getting all heads is

1. 

2. 

3. 

4. 

Q. The probability of getting 53 Fridays in a leap year is .

1. $\frac{4}{7}$
2. $\frac{3}{7}$
3. $\frac{2}{7}$
4. $\frac{1}{7}$