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The definition of probability is the degree to which something is likely to occur. An impossible event is an event with no chance of occurring.
Hence, the probability of an impossible event is zero.
Two coins are tossed simultaneously. The probability of getting at least one head is:
On tossing two coins, following outcomes can be observed: {(H, H),(T, T),(H, T),(T, H)}
Therefore, there are total of 4 possible outcomes
Now, favourable outcomes are {(H,H),(H,T),(T,H)}
Therefore, no. of favourable outcomes are 3
Hence, P(Getting at least one head) = 3/4.
In a class, 20 students failed in a certain examination. If the no. of passed students is 80 and 1 student is selected at random, then the probability that the student has passed in the exam is:
P (student passed in the examination)
= 0.8.
A dice is rolled twice, and the outcomes are noted down. The probability of getting even no. as a sum is:
P (drawing sum as even number)
= 18/36 = 1/2
The probability of getting odd number as a unit place digit is:
1, 3, 5, 7 and 9 are odd numbers
∴ Required probability
= 107/200.
A coin is tossed 1000 times, if the probability of getting a tail, 3/8 how many times head is obtained?
Tail is obtained (3/8 × 1000) times = 375 times.
∴ Head is obtained (1000 – 375) = 625 times.
The distribution of marks of 90 students are as follows:
The probability that a student obtained 40 or more marks is:
P (student getting 40 or more marks)
One card is drawn from a well shuffled deck of 52. What is the probability of drawing a red card?
P (getting a red card) = 26/52 = 1/2
There are 36 students in a class of whom 20 are boys and remaining are girls. What is the probability that a student chosen is a girl?
P (student chosen is girl)
Two dice are thrown simultaneously. What is the probability of getting a doublet?
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) are the doublets
∴ P (getting a doublet) = 6/36 = 1/6.
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