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# The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.

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The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

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09 Aug 2018, 10:13
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Difficulty:

25% (medium)

Question Stats:

69% (01:14) correct 31% (01:19) wrong based on 61 sessions

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The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday. What is the probability that it rains in Dennyville on at least one of these two days?

1. 120%

2. 88%

3. 76%

4. 60%

5. 32%

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Re: The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

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09 Aug 2018, 10:20
2
The chance of rain in Dennyville on Monday is 40%

=> The chance of NO rain in Dennyville on Monday is 100-40 = 60%

The chance of rain in Dennyville on Tuesday is 80%

=> The chance of NO rain in Dennyville on Tuesday is 100-80 = 20%

Required probability is the sum of following 3 cases

case 1 -> Rain on Monday and no rain on Tuesday

case 2 -> No rain on Monday and rain on Tuesday

case 3 -> Rain on both Monday and Tuesday

Case 1 probability = $$\frac{40}{100} * \frac{20}{100} = \frac{8}{100}$$

Case 2 probability = $$\frac{60}{100} * \frac{80}{100} = \frac{48}{100}$$

Case 3 probability = $$\frac{40}{100} * \frac{80}{100} = \frac{32}{100}$$

Sum of all 3 probabilities = $$\frac{8}{100} + \frac{48}{100} + \frac{32}{100}$$

= $$\frac{88}{100} = 88%$$

Hence option B
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The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

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10 Aug 2018, 08:25
AkshdeepS wrote:
The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday. What is the probability that it rains in Dennyville on at least one of these two days?

1. 120%

2. 88%

3. 76%

4. 60%

5. 32%

P(at least one) = 1 - P(none)
For "at least one" probability questions, it is usually easier to find the probability of NONE and subtract from 1. We have only one case to consider: 0 days of rain.

The opposite of "at least one" is "none."

P(at least one) = 1 - P(none)

P(none) = P(no rain on M and no rain on Tu)

P(no rain on M and no rain on Tu):
$$(0.60 * 0.20) = (0.12)$$

Thus P(at least one day) = 1 - P(0 days):
$$(1 - 0.12) = .88 = 88$$ %

Explanation
If the events are independent (probability or outcome on Monday does not affect probability or outcome on Tuesday), and

"Success"
= it DOES rain on at least one day
= P(A), then

"Failure" (no successes)
= it DOES NOT rain on at least one day
= it rains on 0 days
= P(not A)

The complement rule applies
P(A) + P(not A) = 1
P(A) = 1 - P(not A)
P(at least 1 success) = 1 - P(no successes)

--If "success" contains multiple possibilities, and
-- the problem asks for "at least" or "at most," then
-- try finding the probability that success does not occur, i.e., try finding the probability of failure. Subtract from 1.

The result is the probability of "at least one."

For an overview of "at least one," see
Probability - At least, on GMAT Club, here.
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The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.   [#permalink] 10 Aug 2018, 08:25
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