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A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. The probability that the ball is neither white nor black is:
Number of red balls = 6
Number of white balls = 8
Number of green balls = 5
Number of black balls = 3
Total number of balls = 6 + 8 + 5 + 3 = 22
P (neither white nor black ball) = P (red or green ball)
Hence the probability of neither white nor black is 1/2.
A bag contains 5 red and some black balls. If the probability of drawing a black ball is thrice that of a red ball, the number of black balls in the bag is:
Let the number of black balls in the bag be x
∴
⇒ x = 15
Hence, there are 15 blue balls in the bag.
A box contains 200 balls out of which 20 are defective. A bulb is drawn at random. What is the probability of drawing a non–defective bulb?
P (getting a non–defective bulb)
The sum of probabilities of all the outcomes of an experiment is:
P (occurrence of a event) + P (non occurrence of event) = total probability = 1
A bag contains cards marked with numbers 51, 52, …., 100. A number is selected at random. What is the probability of getting a number which is not a multiple of 5?
Number of multiples of
∴ Required probability
One card is drawn from a well–shuffled deck of 52 cards. The probability of drawing a red face card is:
King, queen and jack are known as face cards
Number of red face cards = 2 × 3 = 6
∴ Required probability = 6/52 = 3/26
Two dice are rolled simultaneously. Find the probability of getting their product as a odd number.
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) (5, 5) (5, 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)
Even × odd = even and odd × odd = odd.
∴ For product to be odd, both numbers should be odd.
∴ Required probability = 9/36 = 1/4.
Probability defines the likelihood of occurrence of an event.
An event whose occurrence is 100% sure, those events are called certain events.
The probability of such an event is always 1.
Example: The probability of getting a number between 1 to 6 when rolling a die is a certain event.
Thus, the probability of an event that is certain to occur is 1.
4 coins are tossed simultaneously. The probability of getting all tails is;
The probability of getting all tails
A dice is rolled 600 times and the occurrence of the outcomes are given below:
The probability of getting a composite number is:
P (composite number)
{∵ composite numbers are 4 and 6}
The unit place digit of 200 people’s mobile number is observed, and the following table is plotted:
A number is chosen at random. The probability that its unit place has prime number is:
Prime numbers are 2, 3, 5, 7
∴ Sum of frequencies = 23 + 20 + 11 + 30 = 84
∴ Required probability = 84/200 = 42/100 = 0.42
A dice is rolled twice. Find the probability of getting a prime number as a sum.
Prime numbers which can get as a sum of the numbers on dice are 2, 3, 5, 7, 11
∴ Required probability
A coin is tossed 1000 times and the following frequencies are observed:
Head: 455, Tail: 545
The probability for getting tail is:
Total outcomes = 1000
Frequency of Head = 455
Frequency of Tail = 545
Probability of getting head = 455/1000 = 0.455
Probability of getting tail = 545/1000 = 0.545 or 109/200.
One card is drawn from a wellshuffled deck of 52 cards. What is the probability of getting a king?
No. of cards in pack = 52
P (getting a king)
= 4/52 = 1/13.
Three coins are tossed simultaneously. The probability of getting exactly 2 heads is:
Formula: Probability = Number of favorable outcomes/Total number of outcomes
When three coins are tossed then the outcome will be any one of these combinations
(TTT, THT, TTH, THH, HTT, HHT, HTH, HHH)
So, the total number of outcomes is 8
Now, for exactly two heads, the favorable outcome is (THH, HHT, HTH)
We can say that the total number of favorable outcomes is 3
Again, from the formula
Probability = Number of favorable outcomes/Total number of outcomes
Probability = 3/8
∴ The probability of getting exactly two heads is 3/8.
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