Jasmine Grover Content Strategy Manager
Content Strategy Manager
Probability is the prediction of the happening of an event. It is based on previous records and possible outcomes. When we say that there is some probability that it might rain today, we are making assumptions on the basis of previous weather records, we are not assuring for that particular event.
Some terminologies
- Outcome: The result of any random experiment is known as the outcome. Ex: When a coin is tossed and got tail in it. It will be called the outcome of that experiment.
- Sample Space: It is a set of all possible outcomes for a random experiment. Ex: When a coin is tossed, we can get either a head or a tail. These are called the sample space.
- Event: In the case of an experiment, an event is a set of possible outcomes. Ex: On rolling a dice, if we want 6 on the upper face and did not get it. Then the event is the random experiment whose result is not 6.
- Probability Formula: It is defined as the possibility of an event to happen is equal to the total number of favourable outcomes to the total number of outcomes.
P(E)= Total number of favourable outcomes/Total number of outcomes
Q1) The probability of an event equal to zero is called:
- Unsure event
- Sure event
- Impossible event
- Independent event
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Answer: c) Impossible event
Explanation: It is defined as the probability of an event that cannot happen or is not possible which is an impossible event. An impossible event cannot occur. Example: The sun is rising from the west, rolling of a nine on a six-sided die, while flipping a coin both head and tail cannot come together. All these events are not possible, so these are called impossible events.
Q2) The probability that cannot exist among the following:
- 2/3
- -1.5
- 15%
- 0.7
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Answer: b) -1.5
Explanation: The probability of an event always lies between 0 and 1, where 0 indicates the impossibility of an event and 1 indicates certainty. Higher probability shows that the event has more chances to occur whereas lower probability shows that the event has very less chance to occur. Here, -1.5 can never come under the probability of an event as it is not in between 0 and 1.
Q3) A bag has 3 red balls & 5 green balls. If we take any ball from the bag, then what is the probability of getting only a red ball?
- 3
- 8
- 3/8
- 8/3
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Answer: c) 3/8
Explanation: Number of red balls = 3
Number of green balls =5
Total number of balls in the bag = 3+5 = 8
The formula is:
Probability of getting red balls only= Number of red balls/Total number of balls
As the value of red balls and the total number of balls are given above. We have to put the value in place of the formula,
Probability of getting red balls only = 3/8
Hence, the probability of getting red balls only is 3/8.
Q4) A bag has 5 white marbles, 4 purple marbles, and 8 red marbles. If a marble is chosen randomly, then what is the probability of not getting purple marble?
- 0.5
- 0.66
- 0.08
- 0.77
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Answer: d) 0.77
Explanation: Total number of purple marbles = 4
Total number of other marbles apart from purple = white marbles (5) + red marbles (8)
Total number of marbles in the bag = 5+8+4 = 17
Probability of not getting purple marbles = 5+8/17 = 13/17
Hence, the probability of not getting purple marbles is 0.77
This question can also be solved with different methods i.e., P(not E) = 1- P(E)
Q5) A dice is thrown in the air. The probability of getting odd numbers is :
- ½
- 3/2
- 3
- 4
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Answer: a) ½
Explanation: A dice has six faces with values 1,2,3,4,5 and 6. There are 3 even numbers and 3 odd numbers.
The probability of getting odd numbers is = Number of odd digits faces in a dice/Total number of faces in a dice = 3/6 =1/2
For getting the even numbers the process is similar. Number of even digits faces in a dice/Total number of faces in a dice = 3/6 =1/2
Hence, the probability of getting only odd numbers is ½.
Q6) If we throw two coins in the air, then the probability of getting both tails will be:
- ½
- ¼
- 2
- 4
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Answer: b) ¼
Explanation: A coin has two sides, head and tail. The total outcome of a coin is 2.
When two coins are tossed simultaneously, the total outcomes will be 2*2=4
The outcomes are: HH,HT,TH,TT
The probability of getting both tails is only 1 (TT).
Probability of getting both tails = Total no of both tails/ Total no of outcomes = ¼
Hence, the probability of getting both tails is ¼.
Q7) If two dice are thrown in the air, the probability of getting sum of 3 will be:
- 2/18
- 3/18
- 1/18
- 1/36
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Answer: c) 1/18
Explanation: The total outcome of dice when it is thrown in the air is 6.
Likewise, when two dices are thrown simultaneously then their outcomes will be 6*6=36.
The outcomes are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
The probability of getting sum 3 is possible with (1,2) or (2,1)
Probability= Sum of 3 from the outcome/Total no of outcomes =2/36 =1/18.
Hence, the probability of getting 3 is 1/18.
Q8) A card is drawn from a set of 52 cards. Find the probability of getting a queen card.
- 1/26
- 1/13
- 4/53
- 4/13
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Answer: b) 1/13
Explanation: There is a total 52 number of cards. 52 cards are divided into 4 suits: 13 Spade, 13 Heart, 13 Club, 13 Diamond. In each suite, there are 1 Ace, 1 King, 1 Queen, 1 Jack.
Total 4 Aces, Kings, Queens and Jacks are there in the playing cards.
Now, according to the question total number of queen cards=4
The probability of getting queen card= Total number of queen cards/Total number of playing cards =4/52 =1/13
Hence, the probability of getting a queen card is 1/13.
Q9) A card is selected at random from a well-shuffled deck of 52 playing cards. The probability of its being a face card is:
- 3/13
- 4/13
- 6/13
- 9/13
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Answer: a) 3/13
Explanation: Total number of outcomes = 52
As mentioned in the above question, from 52 playing cards Jack, queen and king together are called face cards. These 12 cards are also called “The Court”.
Total number of face cards = 4 Jacks + 4 Queens + 4 Kings = 12 cards
Probability of getting a face card= Total number of face cards/Total number of outcomes = 12/52 =3/13
Hence, the probability of getting a face card is 3/13.
Q10) The probability that a non-leap year selected at random will contain 53 Sundays is:
- 1/7
- 2/7
- 3/7
- 5/7
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Answer: a) 1/7
Explanation: Non leap year= 365 days
A year consists of 52 weeks and a day. In 52 weeks there will be 52 Sundays.
And the remaining 1 day can be a Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday.
Total number of possible outcomes = 7
Total number of favourable outcomes (for 1 day) = 1
Probability of getting 53 Sundays = Total number of favourable outcomes/Total number of possible outcomes = 1/7
Hence, the probability of getting 53 Sundays is 1/7.
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