In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student?

Question

Kennedy Adams · Accepted Answer

# 19/30.#

Let, #E=#the Event that a randomly chosen student is a girl, &,

#F=#the Event that a randomly chosen student is A.

Then, the Reqd. Prob.,

#=P(EuuF)=P(E)+P(F)-P(EnnF)......................(star).#

#P(E):-#

There are #30# students in the class, so, #1# student can be

chosen in #30# ways.

In the class, there are #17# girls in the class, &, #1# girl can be

chosen in #17# ways.

#:. P(E)=17/30....................................(star^1).#

Similarly, #P(F)=5/30........................(star^2).#

# P(EnnF):-#

Let us note that, #EnnF# denotes the event that the randomly

chosen student is an A girl.

Since there are #3# A girl students in the class, we have,

# P(EnnF)=3/30.......................................(star^3).#

Using #(star^1)" to "(star^3)# in #(star),# we have,

#"The Reqd. Prob.="17/30+5/30-3/30=19/30.#

Enjoy Maths.!

Eva Adamson · Answer

undefined To calculate the probability of choosing a girl or an A student, you need to add the probabilities of choosing a girl and choosing an A student, and then subtract the probability of choosing a girl who is also an A student.

Probability of choosing a girl: 17 girls out of 30 students = 17/30
Probability of choosing an A student: 5 A students out of 30 students = 5/30
Probability of choosing a girl who is also an A student: 3 girls out of 5 A students = 3/5

Probability of choosing a girl or an A student = (Probability of choosing a girl) + (Probability of choosing an A student) - (Probability of choosing a girl who is also an A student)
Probability of choosing a girl or an A student = (17/30) + (5/30) - (3/5)
Probability of choosing a girl or an A student = 0.567 or 56.7%