Question

If 75% of a class answered the first question correctly. 55% answered the second question correctly and 20% answered beither of the questions correctly. What % answered both the question correctly

Answer 1

% of class answered both the question correctly is 50%.

Step-by-step explanation:

We are given that 75% of a class answered the first question correctly. 55% answered the second question correctly and 20% answered neither of the questions correctly.

Let Probability that class answered the first question correctly = P(F) = 0.75

Probability that class answered the second question correctly = P(S) = 0.55

Probability that class answered neither of the questions correctly = $P(\bar F \bigcap \bar S)$ = 0.20

And we have to find that how much % of class answered both the question correctly.

Now, as we know that;

Probability that class answered neither of the questions correctly = 1 - Probability that class answered at least one question correctly

Or in simple terms;  $P(\bar F \bigcap \bar S) = 1 - P(F \bigcup S)$

                                 $P(F \bigcup S) = 1 - P(\bar F \bigcap \bar S)$

                                 $P(F \bigcup S) = 1 - 0.20$ = 0.80

So, Probability that class answered at least one question correctly is 0.80 .

Now, % of class that answered both the question correctly = $P(F \bigcap S)$

Since,   $P(F \bigcup S) = P(F) + P(S) - P(F \bigcap S)$

                  0.80 = 0.75 + 0.55 - $P(F \bigcap S)$

             $P(F \bigcap S)$ = 1.30 - 0.80 = 0.50

Therefore, 50% of the class answered both the question correctly.