Math

QuestionFinlay has some cards. Each card has a colour on it. If he chooses a card at random, then P(P( yellow )=38)=\frac{3}{8} and P(P( black )=116)=\frac{1}{16}.
Calculate PP (neither yellow nor black). Give your answer as a fraction in its simplest form.

Studdy Solution
Calculate the probability of choosing neither yellow nor black by subtracting the probability of choosing either yellow or black from 1:
P(neither yellow nor black)=1P(yellow or black) P(\text{neither yellow nor black}) = 1 - P(\text{yellow or black}) =1716 = 1 - \frac{7}{16}
Convert 1 to a fraction with a denominator of 16:
1=1616 1 = \frac{16}{16}
Subtract the fractions:
P(neither yellow nor black)=1616716=916 P(\text{neither yellow nor black}) = \frac{16}{16} - \frac{7}{16} = \frac{9}{16}
The probability of choosing neither yellow nor black is:
916 \boxed{\frac{9}{16}}

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