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3 years ago

1. Space 2. ∅ 3. ↔ LM 4. plane p 5. None of these

Mathematics

1 answer:

mina [271]3 years ago

5 0

De Morgan's law: (A∩B)' = A'∪B'

(S₁∩P)' = S'₁ ∪ P'

S'₁={P} ∪ {S₂}
P' ={ S₁} ∪ {S₂}

S'₁ ∪ P' ={P} ∪ {S₂} ∪ { S₁} ∪ {S₂}

(S₁∩P)' = S'₁ ∪ P' = SPACE

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Answer:

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Step-by-step explanation:

Since the trials are independent, this is a binomial distribution:

Recall:

Binomial Distribution --> $P(k)={n\choose k}p^kq^{n-k}$
$P(k)$ denotes the probability of $k$ successes in $n$ independent trials
$p^k$ denotes the probability of success on each of $k$ trials
$q^{n-k}$ denotes the probability of failure on the remaining $n-k$ trials
${n\choose k}=\frac{n!}{(n-k)!k!}$ denotes all possible ways to choose $k$ things out of $n$ things

Given:

$n=10$
$k=4$
$p^k=0.53^4$
$q^{n-k}=(1-0.53)^{10-4}=0.47^6$
${n\choose k}={10\choose 4}=\frac{10!}{(10-4)!4!}=210$

Calculate:

$P(4)=(210)(0.53^4)(0.47^6)=0.1786117069\approx0.179$

Therefore, the probability that the archer will get exactly 4 bull's-eyes with 10 arrows in any order is 0.179

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