Math / Data & Statistics

QuestionPart 6 of 6 Points: $0 \%$ , 9 of 10 points Save
Color blindness is an inherited characteristic that is more common in males than in females. If M represents male and C represents red-green color blindness, using the relative frequencies of the incidences of males and red-green color blindness as probabilities results in the values below. Complete parts (a) through ( $f$ ) below. $P(C)=0.035, P(M \cap C)=0.033, P(M \cup C)=0.487$ (a) Find $P\left(C^{\prime}\right)$ . $P\left(C^{\prime}\right)=0.965$ (Type an integer or a decimal.) (b) Find $P(M)$ . $P(M)=0.485$ (Type an integer or a decimal.) (c) Find $P\left(M^{\prime}\right)$ . $P\left(M^{\prime}\right)=0.515$ (Type an integer or a decimal.) (d) Find $P\left(M^{\prime} \cap C^{\prime}\right)$ . $P\left(M^{\prime} \cap C^{\prime}\right)=0.513$ (Type an integer or a decimal.) (e) Find $P\left(C \cap M^{\prime}\right)$ . $P\left(C \cap M^{\prime}\right)=0.002$ (Type an integer or a decimal.) (f) Find $P\left(C \cup M^{\prime}\right)$ . $P\left(C \cup M^{\prime}\right)=\square_{4}$ (Type an integer or a decimal.)

Studdy Solution

STEP 1

1. We are given the probabilities $P(C) = 0.035$ , $P(M \cap C) = 0.033$ , and $P(M \cup C) = 0.487$ .
2. We need to find the probabilities of complementary and combined events using the given data.

STEP 2

1. Calculate $P(C')$ .
2. Calculate $P(M)$ .
3. Calculate $P(M')$ .
4. Calculate $P(M' \cap C')$ .
5. Calculate $P(C \cap M')$ .
6. Calculate $P(C \cup M')$ .

STEP 3

Calculate the probability of the complement of $C$ , $P(C')$ :
$P(C') = 1 - P(C) = 1 - 0.035 = 0.965$

STEP 4

Calculate the probability of $M$ using the formula for the union of two events:
$P(M \cup C) = P(M) + P(C) - P(M \cap C)$
Rearrange to solve for $P(M)$ :
$P(M) = P(M \cup C) - P(C) + P(M \cap C)$
$P(M) = 0.487 - 0.035 + 0.033 = 0.485$

STEP 5

Calculate the probability of the complement of $M$ , $P(M')$ :
$P(M') = 1 - P(M) = 1 - 0.485 = 0.515$

STEP 6

Calculate the probability of the intersection of the complements, $P(M' \cap C')$ :
Using the formula for the complement of the union:
$P(M' \cap C') = 1 - P(M \cup C)$
$P(M' \cap C') = 1 - 0.487 = 0.513$

STEP 7

Calculate the probability of $C \cap M'$ :
Using the formula for the intersection of complements:
$P(C \cap M') = P(C) - P(M \cap C)$
$P(C \cap M') = 0.035 - 0.033 = 0.002$

STEP 8

Calculate the probability of the union of $C$ and $M'$ :
Using the formula for the union:
$P(C \cup M') = P(C) + P(M') - P(C \cap M')$
$P(C \cup M') = 0.035 + 0.515 - 0.002 = 0.548$
The probability $P(C \cup M')$ is:
$\boxed{0.548}$

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Studdy Solution

STEP 1

1. We are given the probabilities $P(C) = 0.035$ , $P(M \cap C) = 0.033$ , and $P(M \cup C) = 0.487$ .
2. We need to find the probabilities of complementary and combined events using the given data.

STEP 2

1. Calculate $P(C')$ .
2. Calculate $P(M)$ .
3. Calculate $P(M')$ .
4. Calculate $P(M' \cap C')$ .
5. Calculate $P(C \cap M')$ .
6. Calculate $P(C \cup M')$ .

STEP 3

Calculate the probability of the complement of $C$ , $P(C')$ :
$P(C') = 1 - P(C) = 1 - 0.035 = 0.965$

STEP 4

Calculate the probability of $M$ using the formula for the union of two events:
$P(M \cup C) = P(M) + P(C) - P(M \cap C)$
Rearrange to solve for $P(M)$ :
$P(M) = P(M \cup C) - P(C) + P(M \cap C)$
$P(M) = 0.487 - 0.035 + 0.033 = 0.485$

STEP 5

Calculate the probability of the complement of $M$ , $P(M')$ :
$P(M') = 1 - P(M) = 1 - 0.485 = 0.515$

STEP 6

Calculate the probability of the intersection of the complements, $P(M' \cap C')$ :
Using the formula for the complement of the union:
$P(M' \cap C') = 1 - P(M \cup C)$
$P(M' \cap C') = 1 - 0.487 = 0.513$

STEP 7

Calculate the probability of $C \cap M'$ :
Using the formula for the intersection of complements:
$P(C \cap M') = P(C) - P(M \cap C)$
$P(C \cap M') = 0.035 - 0.033 = 0.002$

STEP 8

Calculate the probability of the union of $C$ and $M'$ :
Using the formula for the union:
$P(C \cup M') = P(C) + P(M') - P(C \cap M')$
$P(C \cup M') = 0.035 + 0.515 - 0.002 = 0.548$
The probability $P(C \cup M')$ is:
$\boxed{0.548}$

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Studdy Solution

STEP 1

1. We are given the probabilities P(C)=0.035 P(C) = 0.035 P(C)=0.035, P(M∩C)=0.033 P(M \cap C) = 0.033 P(M∩C)=0.033, and P(M∪C)=0.487 P(M \cup C) = 0.487 P(M∪C)=0.487.2. We need to find the probabilities of complementary and combined events using the given data.

STEP 2

1. Calculate P(C′) P(C') P(C′).2. Calculate P(M) P(M) P(M).3. Calculate P(M′) P(M') P(M′).4. Calculate P(M′∩C′) P(M' \cap C') P(M′∩C′).5. Calculate P(C∩M′) P(C \cap M') P(C∩M′).6. Calculate P(C∪M′) P(C \cup M') P(C∪M′).

STEP 3

Calculate the probability of the complement of C C C, P(C′) P(C') P(C′):P(C′)=1−P(C)=1−0.035=0.965 P(C') = 1 - P(C) = 1 - 0.035 = 0.965 P(C′)=1−P(C)=1−0.035=0.965

STEP 4

STEP 5

Calculate the probability of the complement of M M M, P(M′) P(M') P(M′):P(M′)=1−P(M)=1−0.485=0.515 P(M') = 1 - P(M) = 1 - 0.485 = 0.515 P(M′)=1−P(M)=1−0.485=0.515

STEP 6

STEP 7

STEP 8

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1. We are given the probabilities $P(C) = 0.035$ , $P(M \cap C) = 0.033$ , and $P(M \cup C) = 0.487$ .
2. We need to find the probabilities of complementary and combined events using the given data.

1. Calculate $P(C')$ .
2. Calculate $P(M)$ .
3. Calculate $P(M')$ .
4. Calculate $P(M' \cap C')$ .
5. Calculate $P(C \cap M')$ .
6. Calculate $P(C \cup M')$ .

Calculate the probability of the complement of $C$ , $P(C')$ :
$P(C') = 1 - P(C) = 1 - 0.035 = 0.965$

Calculate the probability of the complement of $M$ , $P(M')$ :
$P(M') = 1 - P(M) = 1 - 0.485 = 0.515$