In a classroom of children (10 boys and 8 girls), six students are chosen to go to the blackboard. What is the probability that no boys are chosen?
8/18
To find the probability that no boys are chosen, we need to determine the total number of possible outcomes where no boys are chosen and divide it by the total number of possible outcomes.
Total number of possible outcomes:
Since six students are chosen from a class of 18 (10 boys + 8 girls), the total number of possible outcomes is given by the combination formula: C(18, 6) = 18!/(6!(18-6)!) = 18!/(6!12!) = (18*17*16*15*14*13)/(6*5*4*3*2*1) = 18,564.
Number of outcomes where no boys are chosen:
Since we want no boys to be chosen, we need to choose all 6 students from only the 8 girls. The number of ways to do this can be calculated using the combination formula: C(8, 6) = 8!/(6!(8-6)!) = 56.
Probability of no boys being chosen:
The probability is given by the number of outcomes where no boys are chosen, divided by the total number of possible outcomes:
P(no boys) = Number of outcomes where no boys are chosen / Total number of possible outcomes = 56/18,564 ≈ 0.0030.
Therefore, the probability that no boys are chosen is approximately 0.0030, or 0.30%.