An article in Genome Research [An Assessment of Gene Prediction Accuracy in Large DNA Sequences (2000, Vol.

An article in Genome Research [€œAn Assessment of Gene Prediction Accuracy in Large DNA Sequences€ (2000, Vol. 10, pp. 1631€“1642)], considered the accuracy of commercial software to predict nucleotides in gene sequences. The following table shows the number of sequences for which the programs produced predictions and the number of nucleotides correctly predicted (computed globally from the total number of prediction successes and failures on all sequences).

Assume the prediction successes and failures are independent among the programs.

(a) What is the probability that all programs predict a nucleotide correctly?

(b) What is the probability that all programs predict a nucleotide incorrectly?

(c) What is the probability that at least one Blastx program predicts a nucleotide correctly?

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Number of Proportion Sequences GenScan 177 0.93 Blastx default 175 0.91 Blastx topcomboN 174 0.97 Blastx 2 stages 175 0.90 GeneWise 177 0.98 Procrustes 177 0.93