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In an experiment there are only two possible outcomes. The probability of each outcome is \(\dfrac{1}{2} \). It is true ? Give reason
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It is true becouse total no. of outcomes are 2 and for each event probability is
Two dice are thrown simultaneously. List the sample space for this experiment.
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The king, Queen and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. What is the probability of getting a heart?
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P(getting a heart)
A girl tosses a coin 3 times and gets a tail each time. Do you think that the outcome of next toss will be a tail? Justify your answer.
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The outcomes of next toss may or may not be tail, because on tossing a coin, we get head or tail so both are equally liked events.
I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is \(\dfrac{1}{4} \) What is wrong with this conclusion?
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Outcomes of 1 head ,
2 head
Remaining 3 heads
Probability of getting no heads is wrong it would be
A card is drawn at random from an ordinary pack of 52. What is the probability that the card is a black king?
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P(black king)
One number is chosen at random from the whole numbers 1 to 100 inclusive. What is the probability that the number has two digits?
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Number of ways
Number of ways to choose a number
Two dice are thrown together. Find the probability that the sum of the digits showing on the top faces of the dice is less than 5.
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Total outcomes
No. of favourable outcomes
P(less than 5)
Find the probability that the month of February may have 5 Sundays in a leap year.
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There is 29 days in february
4 weeks days
days
Probability
A girl throws a die and squares the number that appears on it. A boy throws two dice once and computes the product of numbers appearing on the dice. Who has the better chance of getting the numbers 36. Give reason.
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Probability of girl
Probability of boy
so boy has better chance of getting the number 36.
A coin is tossed 6 times and on each occasion a head is obtained. Can we say that the probability of getting a head is 1? Give reasons.
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No, If we toss a coin then we get head for tail. So probability is if we toss a coin 6 times so the probability of getting a head is not 1.
Three unbiased coins are tossed together. Find the probability of getting either all heads or all tails.
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Total number of alementry events = 8
Favourable no. of elementry event =1
Probability
Two dice are thrown simultaneously. Find the probability that the difference of the numbers on the two dice is 2.
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Favourable
Probability
A coin is tossed two times. Find the probability of getting at most one head.
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A letter of English alphabet is chosen at random. Determine the probabiliry that the letter is a consonant.
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Total number of alphabets = 26
Total number of consonant = 21
A bag contains 14 balls, of which x are white. If 6 more white balls are added to the bag, the probability of drawing a white ball is \( \dfrac{1}{2}\). Find the value of x
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Total number of balls
P(drawing white ball)
Cards marked with numbers 13, 14, 15, ……… 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the card is :
(a) divisible by 5
(b) a number which is a perfect sq
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Numbers which are divisible by 5 = 10
Total outcomes = 60 – 12 = 48
(i) P(getting a number divisible by 5)
(ii) P(getting a perfect square number)
A die is thrown once. Find the probability of getting :
(a) a prime number
(b) a number less than 6
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(i) Prime number = 2, 3, 5
(ii) Number less than 6 = 1, 2, 3, 4, 5
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at
(a) a prime number ?
(b) a factor of 8 ?
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(i) Prime number = 2, 3, 5, 7
(ii) Total number of events = 8
Factors of 8 = 1, 2, 4, 8
A card is drawn at random from a pack of well shuffled deck of playing cards. Find the probability that the card is :
(a) a king or a jack
(b) a card of spade or an ace
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(i) P(getting a king or a jack)
(ii) Total cards of spade
Total Aces
A bag contains 2 green, 3 red and 4 black balls. A ball is taken out of the bag at random. Find the probability that the selected ball is
(a) not green
(b) not black.
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Total balls = 2 + 3 + 4 = 9
(i) P(not green)
(ii) P(not black)
A bag contains cards numbered from 2 to 26. One card is drawn from the bag at random. Find the probability that it has a number divisible by both 2 and 3.
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Total number of cards = 25
Number divisible by both 2 and 3
= 6, 12, 18, 24
In a leap year, find the probability that there are 53 Tuesdays in the year.
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There are 366 days in a leap year i.e. 52 weeks and 2 days
Total possible cases = 7
Total favourable cases = 2
Probability
One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a red face card.
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Probability of getting a red
face card
Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on their tops is less than or equal to 10.
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Total outcomes = 36
A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.
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There are 26 red cards
Number of card which are neither red nor queen = 52 – (26+2) = 24
A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. Find the probability of getting neither a green ball nor a red ball.
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Total balls = 5 + 8 + 7 = 20 balls
P(neither a green nor red)
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.
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Total no. of balls
Probability of drawing a red ball
Probability of drawings a blue ball
A/Q
No. of blue balls = 15
Two dice are thrown once. Find the probability of obtaining :
(a) a total of 6 of numbers on both dice.
(b) the same number on both dice.
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(i) P(sum of 6)
(ii) P(getting doublet)
From a group of 2 boys and 2 girls, two children are selected at random. What is the sample space representing the event. Find the probability that one boy and one girl is selected.
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Probability
A letter is chosen at random from the English alphabet. Find the probability that it is
(A) a vowel
(B) a consonant
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Total number of letters = 26
(i) P(a vowel)
(ii) P(a consonant)