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The meaning of probability is an eventuality, that is, the happening of an event. It deals with the occurrence of a random event that is likely to happen. The value of probability always comes in between 0 and 1. Its value cannot be less than zero and cannot be more than one. One cannot predict the complete certainty of an event, and one can only predict the proportions of an event to happen. The probability is the possibility of an event that can be determined by dividing the number of favourable outcomes by the number of total outcomes.
Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes
When two dices are thrown, then their possible outcomes are 6 × 6 = 36. Here, there are 36 total outcomes. If the question demands an even or odd number out of these outcomes, they will be called favourable outcomes.
Also read: Probability: Definition, Formula, Types and Problems
Ques 1: The probability of each event, when a coin is tossed 100 times with frequencies: head 40 and tail 60 is
- 0.40 & 0.60
- 0.50 & 0.50
- 0.60 & 0.40
- 0.20 & 0.80
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Explanation:
Suppose A and B are the events of the occurrence of head and tail, respectively.
Probability of Occurrence of Head P (A) = Number of heads/Total number of possible outcomes
P (E) = 40/100 = 0.40
Similarly, P (B) = No of tails/ Total number of possible outcomes
P (B) = 60/100 = 0.60
Hence, the values of heads and tails are 0.40 & 0.60.
Ques 2: If P (E) = 0.30, then the probability of event E not occurring will be
- 0.30
- 0.70
- 0.50
- 0.60
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Answer: (2) 0.70
Explanation:
As we know that P (E) + P (not E) = 1
Now we will put the values accordingly,
0.30 + P (not E) = 1
P (not E) = 1 − 0.30 = 0.70
In the probability, the value of the resultant cannot be more than 1.
Hence, the value of P (not E) is 0.70.
Ques 3: The probability of drawing an ace card from a deck of red cards is
- 1/52
- 1/26
- 1/13
- 2/13
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Answer: (4) 2/13
Explanation:
There are 52 cards in a deck.
Out of them, 26 are black, and 26 are red.
In 26 red cards, there are 13 hearts and diamonds each.
In 26 black cards, there are 13 spades and clubs each.
And, 1 king, 1 queen, 1 jack and 1 ace are there in every 13 cards. All together, they are called honour cards.
According to the question, the total number of red cards = 26
Total number of aces in a deck of cards = 4
P (E) = Total number of aces/Total number of red cards = 4/26 = 2/13.
Ques 4: A batsman hits boundaries for 5 times out of 40 balls. Find out the probability that he did not hit the boundaries.
- 1/5
- 7/8
- 2/5
- 1/8
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Answer: (b) 7/8
Explanation:
Number of boundaries = 5
Total number of balls = 40
Number of balls without boundaries = 40 – 5 = 35
Probability of not hitting the boundaries = 35/40 = 7/8.
Hence, the probability that he did not hit any boundary is 7/8.
Ques 5: Consider picking a card from a deck of 52 cards. What is the probability of getting a queen of black suits?
- 1/26
- 2/13
- 1/52
- 3/13
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Answer: (a) 1/26
Explanation:
There are 52 cards in a deck. As mentioned in the above question, the number of red and black cards are 26 each.
Out of them, there is 1 card of king, queen, jack and ace from every 13 cards.
Number of a queen in black suits = 2
Total number of cards = 52
P (E) = Total number of queens of black suit/Total number of cards from the deck
= 2/52 = 1/26.
Ques 6: Find out the probability of a selected number is a multiple of 3 from the numbers 1, 2, 3, 4, 5, 6, ……14, 15, 16, 17, 18.
- 1/5
- 1/6
- 5/13
- 1/3
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Answer: (4) 1/3
Explanation:
Sample Space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Multiples of 3 from the sample space = 3, 6, 9, 12, 15, 18
P (E) = Number multiple of 3/Total numbers given in the sample space
= 6/18 = 1/3
Hence, a multiple of 3 from the numbers is 1/3.
Ques 7: What is the probability of getting a king or ace from the deck of 52 cards?
- 1/26
- 2/13
- 3/26
- 1/52
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Answer: (2) 2/13
Explanation:
Total number of cards from the deck = 52
Total number of kings from the deck of cards = 4
Total number of aces from the deck of cards = 4
Probability of getting both king or ace = 4 + 4 =8
P (E) = Total number of king or ace from the cards/Total number of cards
= 8/52 = 2/13
Hence, the probability of getting a king or ace from the cards is 2/13.
Ques 8: There are 3 blue and 4 red balls in a basket. The probability of getting the red balls is
- 1/2
- 3/7
- 4/7
- 7/7
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Answer: (2) 4/7
Explanation:
Total number of blue balls = 3
Total number of red balls = 4
Total number of balls = 3 +4 = 7
P (E) = Total number of red balls/Total number of balls in the bag
= 4/7
Hence, the probability of getting blue balls is 4/7.
Ques 9: Consider tossing two coins together. Find the probability of getting at least one head.
- 1/2
- 1/3
- 1/4
- 3/4
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Answer: (4) 3/4
Explanation:
When two coins are tossed, their sample space are = HH, HT, TH, TT
Probability of getting at least one head (minimum one head and maximum of 2 heads should be there)
Number of total outcomes = 4
Total number of at least one head = 3
P(E) = Total number of at least one head/Total number of possible outcomes
= 3/4
Hence, the probability of getting at least one head is 3/4.
Ques 10: There are 3 red balls, 4 green balls, and 5 black balls in a basket. The probability of not getting the red balls is
- 1/4
- 1/3
- 5/12
- 3/4
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Answer: (4) 3/4
Explanation:
Total number of balls all together = 3 + 4 + 5 = 12
Total number of red balls = 3
Total number of green balls = 4
Total number of black balls = 5
Now, the total number of non-red balls = 9
P (E) = Total number of non-red balls/Total number of balls
= 9/12 = 3/4.
Hence, the total number of non-red balls is 3/4.
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