Page 324 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\14_Chapter\14_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

Note that P(E) is a numerical measure whose value lies from 0 to 1.

Thus, 0 ≤ P(E) ≤ 1
Example 22: At a car parking, there are 80 vehicles, 30 of which are cars, 30 are vans and the
remaining are lorries. If every vehicle is equally likely to leave, find the probability of:

(a) vans leaving first (b) lorries leaving first

(c) cars leaving second if either a lorry or a van had left first.
Solution: Total number of vehicles = 80

Number of cars = 30
Number of vans = 30

Number of lorries = 80 – 30 – 30 = 80 – 60 = 20
30 3
(a) Probability of vans leaving first = =
80 8
20 1
(b) Probability of lorries leaving first = =
80 4
(c) If either a lorry or a van had left first, then there would be 79 vehicles remaining,
30 of which are cars.
30
\ Probability of cars leaving after either a lorry or a van had left =
79
Example 23: Head is obtained 30 times when a coin is tossed 50 times at random. Find the
probability of getting:
(a) a head (b) a tail

Solution: Number of heads = 30
Total number of trials = 50
Number of tails = (50 – 30) = 20
number of heads 30 3
(a) P (getting a head) = = =
total number of trials 50 5

number of tails 20 2
(b) P (getting a tail) = = =
total number of trials 50 5

Example 24: A survey shows 35 girls out of 100 girls like football and rest dislike it. Out of these
girls, one girl has been chosen at random. What is the probability that the chosen girl:
(a) likes football? (b) dislikes football?
Solution: Total number of girls = 100
Number of girls who like football = 35
Number of girls who dislike football = 100 – 35 = 65

35 7
(a) P (chosen girl who likes football) = =
100 20
65 13
(b) P (chosen girl who dislikes football) = =
100 20

Mathematics-7 322