Question

A club has 25 members, 20 boys and 5 girls. Two members are selected at random to serve as president and vice president. What is the probability that both will be girls?.

Answer 1

The probability that both will be girls is 1/30.

What is probability?

Probability is a branch of mathematics that deals with the numerical description of how likely an event will occur or not.

To find the probability of both girls as president and vice president, first, we need to find the probability of picking a girl as the president and then also find the probability of picking a girl as the vice president and multiply both together.

• The probability of picking a girl as the president(Pr(pres) = Total numbers of girls(n)/Total members in the club(M)
• Pr(pres) = n/M............Equation 1

From the question,

Given:

• M = 25
• n = 5

Substitute into equation 1

• Pr(Pres) = 5/25
• Pr(Pres) = 1/5.

Also, we need to find the probability of selecting a girl as the vice president.

• Pr(v.p) = (n-1)/(M-1)

Where:

• Pr(v.p) = Probability of selecting a girl as the vice president
  

• Pr(v.p) = (5-1)/(25-1)
• Pr(v.p) = 4/24
• Pr(v.p) = 1/6

Finally,

• The probability that both will be girls is = (1/5)(1/6)
• The probability that both will be girls = 1/30

Hence, The probability that both will be girls is 1/30.
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