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Semenov [28]
3 years ago
8

Spike is not a terribly bright student. His chances of passing chemistry are 0.35; mathematics, 0.40; and both, 0.12. Are the ev

ents "Spike passes chemistry" and "Spike passes mathematics" independent? What is the probability that he fails both subjects?
Mathematics
1 answer:
Feliz [49]3 years ago
8 0

Answer:

The events "Spike passes chemistry" and "Spike passes mathematics" are not independent.

The probability that he fails both subjects = 0.37

Step-by-step explanation:

The probability of Spike passing Chemistry = P(Chemistry) = 0.35

The probability of Spike passing Mathematics = P(Mathematics) = 0.40

The probability of Spike passing both Chemistry and Mathematics = P(Chemistry,Mathematics) = 0.12

For the events "Spike passes chemistry" and "Spike passes mathematics" to be independent, P(Chemistry,Mathematics) should be equal to P(Chemistry) * P(Mathematics)

But P(Chemistry) * P(Mathematics)=0.35*0.40 =0.14

So the two events are not independent.

The Probability that he passes Chemistry or Mathematics is given by P(Chemistry) + P(Mathematics) - P(Chemistry,Mathematics)

= 0.35+0.40-0.12=0.63

So the probability that he fails both subjects is the complement of this, namely (1 - 0.63) = 0.37

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A total of 1,716 selections of the 7 flowers are possible.

Step-by-step explanation:

Step 1:

There are 13 flowers from which Jeanine Baker plans to use 7 of them.

To determine the number of selections that are possible we use combinations.

The formula for combinations is; ^{n} C_{r}=\frac{n !}{(n-r) ! r !}.

Step 2:

In the given formula, n is the total number of options and r is the number of options to be selected.

For this question, n = 13 and r=7.

So ^{13} C_{7}=\frac{13 !}{(13-7) ! 7 !} = \frac{13 !}{(6) ! 7 !} = 1,716.

So a total of 1,716 selections are possible.

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