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The probability that Maria will eat breakfast on any given day is 0.5.

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Bunuel
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The probability that Maria will eat breakfast on any given day is 0.5. [#permalink] New post   07 Jul 2021, 02:15
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The probability that Maria will eat breakfast on any given day is 0.5. The probability that Maria will wear a sweater on any given day is 0.3. The two probabilities are independent of each other. What is the probability that Maria eats breakfast or wears a sweater?

A. 0.15
B. 0.35
C. 0.65
D. 0.75
E. 0.8
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C
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vishuvashishth
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Re: The probability that Maria will eat breakfast on any given day is 0.5. [#permalink] New post   10 Jul 2021, 02:00
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Solution:

It is given that

Probability that Maria will eat breakfast on any given day, which means: P(Breakfast)= 0.5

Probability that Maria will wear sweater on any given day is 4747, which means: P(sweater)=0.3

We are asked the probability that Gary eats breakfast or wear sweater on a particular day, which means we are asked the value of P(breakfast or sweater)

Now we already know, for 2 events A and B: P((A or B)=P(A)+P(B)−P(AB)

So we can write: 0.5 + 0.3 - (0.5 * 0.3)
=> on solving, 0.65.

Answer C.
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Re: The probability that Maria will eat breakfast on any given day is 0.5. [#permalink] New post   10 Jul 2021, 02:16
P (Breakfast) = 0.5
P (Sweater) = 0.3
P (breakfast and sweater) = 0.5 * 0.3 = 0.15
P (breakfast or sweater) = 0.5 + 0.3 - 0.15 = 0.65

Hence, the correct answer is (C).
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Re: The probability that Maria will eat breakfast on any given day is 0.5. [#permalink] New post   10 Jul 2021, 07:59
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Maria eats breakfast or wears a sweater: Breakfast + Sweater - Both

Both (independent): 0.5 * 0.3 = 0.15

Maria eats breakfast or wears a sweater: 0.5 + 0.3 - 0.15 = 0.65

Answer C
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Re: The probability that Maria will eat breakfast on any given day is 0.5. [#permalink] New post   16 Dec 2023, 14:16
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I understand the two are independent however may I know what's the rationale of deducting the probability of co-existence?
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Re: The probability that Maria will eat breakfast on any given day is 0.5. [#permalink]
16 Dec 2023, 14:16
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