Given a spinner with four sections of equal size labeled

Question

Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times?

A. 15/16
B. 9/16
C. 1/2
D. 1/4
E. 1/8

Bunuel · Accepted Answer

The probability of:
Getting A  at leas once  after spinning the spinner two times is 1-3/4*3/4=7/16;
Getting A  only once  after spinning the spinner two times is 1/4*3/4+3/4*1/4=6/16;
NOT getting A on both spins (so no AA) is 1-1/4*1/4=15/16.

Hope it's clear.

Bunuel · Answer

The probability of NOT getting an A after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).

Answer: B.

ashish8 · Answer

Bunel, if you don't mind I want to expand on this problem for other probability concepts.

A. If I was to do 1 - (1/4*1/4) = 15/16.....This should be the right answer to what type of question?
C. 1/4 + 1/4 = 1/2, I assume this would be the right answer for "Probability of hitting A on any one of the two tries"?

jayaddula · Answer

I am going to give it a shot, hopefully someone can confirm/correct me. 
For A - that will be the right answer if the question were, what is the probablity if the hits atleast once if spun twice?
p(e) = 1 - (p(no A at all)

For B - that will be right, if the question were, what is the probality if spinner hit A on first spin or second spin?

ashish8 · Answer

Jay wouldn't the probability of A at least once be, 1 - Probability of NOT A = 1 - (3/4*3/4) = 1 - 9/16 = 7/16 ?

akrish1982 · Answer

it should be (1 - 1/4) * (1 - 1/4), 
not 1 - (1/4*1/4)

this is because both need to happen simultaneousluy, so we need to multiply. if both can happen idepedently, we can add.

KarishmaB · Answer

The right answer is (1/4) + (1/4) - (1/4)*(1/4) = 7/16
and the right question is: What is the probability that you get A at least once? or What is the probability of getting A on any one of the two tries or on both?

You subtract the probability of getting A on both spins because you have double counted it. Think SETS. The first (1/4) includes the probability of 'A on both spins'. The second (1/4) also includes the probability of 'A on both spins'. So you need to subtract it once.

PiyushK · Answer

Meaning is confusing ... after spinning 2 times .. means third time or more.. or spinning spinner by hand 2 times..

KarishmaB · Answer

"Not getting A after spinning 2 times" means not getting A in either of the two spins.

colorblind · Answer

Hey  Bunuel ,

what is the difference between "NOT getting an A after spinning the spinner two times" and "NOT getting A on both spins"?

iqahmed83 · Answer

Hey guys! Don't quite understand the logic on Bunuels post:

Getting A only once after spinning the spinner two times is 1/4*3/4+3/4*1/4=6/16;

colorblind · Answer

Either get   {"A" in the first spin and "non A" in the second spin}   OR get   {"non A" in the first spin and "A" in the second spin}

Hence:
 {(P of A) & (P of non A)}  or  {(P of non A) & (P of A)}

nks2611 · Answer

hii , karishma , can you guide me where am i wrong in these solutions ... 1 p(A or B) = 1/4+1/4-1/4*1/4= 7/16 now we can calculate not getting A that will be 1-7/16=9/16 as it is the answer 2. to me why is this wrong this method 1-1/4*1/4=15/16 for the above problem just because we are asked to calculate the probability of not getting A on both the tires,that's why and this solution will work if we are asked to calculate at least one . let me know if i am missing anything.../ thanks In advance

KarishmaB · Answer

If you are talking about the result after spinning two times, the probability will be multiplied. You spin once, AND you spin again. So it is not P(A or B). It is P(A and B)

1/4 is the probability of getting A on a spin.

(1/4)*(1/4) is the probability that you will get A on BOTH spins.

Hence, 1 - (1/4)(1/4) = 15/16 is the probability the you will not get A on both spins. You could get A on one spin though.

BrentGMATPrepNow · Answer

Since the 4 sections each have EQUAL sizes, P(getting A on a single spin) = 1/4
So, P(NOT getting A on a single spin) = 1 - 1/4 =  3/4

What is the probability of NOT getting an A after spinning the spinner two times?  
P(neither spin lands on A) = P(no A on 1st spin   AND   no A on 2nd spin)
= P(no A on 1st spin)   x   P(no A on 2nd spin)
=  3/4    x    3/4 
= 9/16
= B

ScottTargetTestPrep · Answer

The probability of not getting an A each spin is ¾. Therefore, the probability of not getting an A twice in two spins is ¾ x ¾ = 9/16.

Answer: B

Basshead · Answer

The probability of not getting A on each spin is 3/4 (as the probability of getting A on a spin is 1/4)

3/4 * 3/4 = 9/16.

ayerhs · Answer

Hey  Bunuel , what is the difference between "NOT getting an A after spinning the spinner two times" and "NOT getting A on both spins"? I am still confused.

Bunuel · Answer

1. NOT getting an A after spinning the spinner two times, means not getting A in either of the two spins = 3/4*3/4=9/16. So, the following 9 cases out of 16:
BB
BC
CB
BD
DB
CC
CD
DC
DD

2. NOT getting A on both spins (so no AA) means anything but AA. So, the following 15 case out of 16:
AB
BA
AC
CA
AD
DA
BB
BC
CB
BD
DB
CC
CD
DC
DD

Hope it helps.

Given a spinner with four sections of equal size labeled

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Given a spinner with four sections of equal size labeled

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards