GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 14:03 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1685
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

Show Tags

6 00:00

Difficulty:   25% (medium)

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

HideShow timer Statistics

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%

_________________
"Do not watch clock; Do what it does. KEEP GOING."
MBA Section Director V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2590
GPA: 4
WE: Engineering (Computer Software)
Re: The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

Show Tags

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
_________________
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3548
The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.  [#permalink]

Show Tags

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.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life. The chance of rain in Dennyville is 40% on Monday and 80% on Tuesday.   [#permalink] 10 Aug 2018, 08:25
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  