Proportionality>Finding Probabilities of Events and Their Complements(TEKS.Math.7.6.E)
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Texas 7th Grade Math › Proportionality>Finding Probabilities of Events and Their Complements(TEKS.Math.7.6.E)
Event A: It rains tomorrow. The probability of rain tomorrow is 0.35. What is $P(\text{not }A)$?
0.35
0.75
0.65
1.35
Explanation
Use complements: $P(\text{not }A)=1-P(A)=1-0.35=0.65$. Check: $0.35+0.65=1$.
Event A: A student passes a test. A student has a 3/4 chance of passing the test. What is $P(\text{not }A)$?
1/4
3/4
4/3
1/2
Explanation
Complements satisfy $P(\text{not }A)=1-P(A)=1-\frac{3}{4}=\frac{1}{4}$. Also, $\frac{3}{4}+\frac{1}{4}=1$.
Event A: A spinner lands on green. The spinner lands on green 60% of spins. What is $P(\text{not }A)$?
60%
0.6
160%
40%
Explanation
Complement probability: $P(\text{not }A)=1-P(A)=100%-60%=40%$ (equivalently $1-0.60=0.40$). Check: $60%+40%=100%$.
Which statement about complements is true?
$P(A)-P(\text{not }A)=1$
$P(A)+P(\text{not }A)=1$
$P(A)+P(B)=1$ for any events $A$ and $B$
$P(\text{not }A)=P(A)$ always
Explanation
By definition, $P(A)$ and $P(\text{not }A)$ are complements and must sum to 1. The other statements are not true in general.
Event A: A basketball player makes the next free throw. The probability of a make is 2/5. What is $P(\text{not }A)$?
2/5
3/5
5/3
1/5
Explanation
Compute the complement: $P(\text{not }A)=1-P(A)=1-\frac{2}{5}=\frac{3}{5}$. Check: $\frac{2}{5}+\frac{3}{5}=1$.