Answer to Question #51597 in Statistics and Probability for ojomona

Question

The probability that kodjo and adogba pass an examination are 3/4 and 3/5 respectively. Find the probability of both boys failing the examination.
a)1/3
b) 3/10
c) 9/20
d) 1/3

Answer 1

Probability that kodgo passes an examination is p1=3/4, hence probability that kodgo fails an examination is q1=1-p1=1-3/4=1/4. Probability that adogba passes an examination is p2=3/5, hence probability that adogba fails an examination is q2=1-p2=1-3/5=2/5. Assume that events "kodgo fails an examination" and "adogba fails an examination" are independent. Then by multiplication rule the probability of both boys failing the examination is q1*q2=(1-p1)(1-p2)=1-(p1+p2)+p1*p2=1/4*2/5=2/20=1/10.