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sukhopar [10]
2 years ago
12

Mrs. Jones buys two toys for her son. The probability that the first toy is defective is 1/3, and the probability that the secon

d toy is defective given that the first toy is defective is 1/5. What is the probability that both toys are defective?
Mathematics
2 answers:
Debora [2.8K]2 years ago
6 0

Answer: \frac{1}{15}

Step-by-step explanation:

Let F denote the event of first  toy is defective and S denote the second toy is defective .

Given: The probability that the first toy is defective P(F)=\frac{1}{3}

The probability that the second toy is defective given that the first toy is defective  P(S|F)=\frac{1}{5}

The formula to calculate the conditional probability is given by :-

P(S|F)=\frac{P(S\cap F)}{P(F)}\\\\\Rightarrow P(S\cap F)=P(S|F)\times P(F)\\\\\Rightarrow\ P(S\cap F)=\frac{1}{3}\times \frac{1}{5}=\frac{1}{15}

Hence, the probability that both toys are defective=\frac{1}{15}

sergeinik [125]2 years ago
3 0

Answer:

Probability=\frac{1}{15}

Step-by-step explanation:

As it is given that

Probability of toy A is defective is =P(A) = \frac{1}{3}

Probability of toy b is defective if A is defective = P (B)=\frac{1}{5}

WE have to find the P(A n B)

By the law of Probability

P(A n B) = P (A).P(B)

putting the values given to us

P(AnB)=\frac{1}{3} * \frac{1}{5}

Probability=\frac{1}{15}

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Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards,
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a) 0.9644 or 96.44%

b) 0.5429 or 54.29%

Step-by-step explanation:

a) The probability that at least 1 defective card is in the sample P(A) = 1 - probability that no defective card is in the sample P(N)

P(A) = 1 - P(N) .....1

Given;

Total number of cards = 140

Number selected = 20

Total number of defective cards = 20

Total number of non defective cards = 140-20 = 120

P(N) = Number of possible selections of 20 non defective cards ÷ Number of possible selections of 20 cards from all the cards.

P(N) = 120C20/140C20 = 0.0356

From equation 1

P(A) = 1 - 0.0356

P(A) = 0.9644 or 96.44%

b) Using the same method as a) above

P(A) = 1 - P(N) .....1

Given;

Total number of cards = 140

Number selected = 20

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Total number of non defective cards = 140-5 = 135

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From equation 1

P(A) = 1 - 0.4571

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8 0
2 years ago
Babe Ruth's 1931 salary was $80,000, Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015. Ruth's
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Answer:

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

Step-by-step explanation:

This question can be solved by a rule of three.

Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015.

This means that $15.2 in 1931 is equivalent to $237 in 2015. So

$15.2 in 1931 - $237 in 2015

$80,000 in 1931 - $x in 2015

15.2x = 237*80,000

x = \frac{237*80,000}{15.2}

x = 1,247,368

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

8 0
2 years ago
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