Question

in a committee of 25 members, each member is proficient either in mathematics or in statics or in both.if 19 of these are proficient in mathematics,16 in statics, find the probability that a person selected from the committee is proficient in both​

Answer 1

Answer:

Solution:

Let the A be the event that the person is proficient in mathematics, and B be the event that the person is proficient in statistics and S be the sample.

∴P(A)=

25

19

​

,P(B)=

25

16

​

 

Since each member is proficient either in mathematics or in statistics or in both.

∴A∪B=S⟹P(A∪B)=P(S)=1.

By addition theorem on probability we have,

P(A∪B)=P(A)+P(B)−P(A∩B)

or, P(A∩B)=P(A)+P(B)−P(A∪B)

or, =

25

19

​

+

25

16

​

−1

or, =

25

35−25

​

or, =

25

10

​

or, =

5

2

​

∴P(A∪B)=

5

2

​

Answer 2

Answer:

10

Step-by-step explanation:

The number of people is 10