In a class there are 10 students who play football and cricket
7 who do not play football or cricket
14 students who play football
21 students who play cricket
find the probability that a student chosen at random plays football and cricket.

The probability that a student chosen at random plays football and cricket is 0.3125 or 31.25 %

Solution:

Given that,

In a class there are 10 students who play football and cricket

14 students who play football

21 students who play cricket

7 who do not play football or cricket

The venn diagram is attached below

From venn diagram attached below,

Find the total number of students

Total = 4 + 10 + 11 + 7 = 32

Thus total number of students are 32

Find the probability that a student chosen at random plays football and cricket:

From venn diagram,

See the intersection of football and cricket

10 play football and cricket

The probability is given as:

Therefore,

Thus the probability that a student chosen at random plays football and cricket is 0.3125 or 31.25 %

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47