In this case, we assume that there are only three alleles for blood type: A, B, and O. Since blood type B has a frequency of 30 out of every 100 people, the frequency of the B allele is 30/100 or 0.30. Similarly, the frequency of the A allele is 40/100 or 0.40.
We can use the fact that the frequencies of all the alleles must add up to 1 to find the frequency of the O allele. That is:
Frequency of A allele + Frequency of B allele + Frequency of O allele = 1
Solving for the O allele frequency:
Frequency of O allele = 1 - Frequency of A allele - Frequency of B allele
Frequency of O allele = 1 - 0.40 - 0.30
Frequency of O allele = 0.30 or 30%
Therefore, the frequency of the recessive type O allele is 0.30 or 30%.