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Similar DS questions on probability

Expert replies
by knight247 » Tue Jun 21, 2011 11:32 pm
3 similar DS problems and 1 PS problem. All based on probability. Unfortunately don't have the OAs


1.In a basket there are only apples, mangoes and oranges. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)There are 40 apples and 90 oranges.
(2)10% of the fruits are apples and 25% of the fruits are oranges.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

2.In a basket there are only apples, mangoes and oranges. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)The probability that a fruit randomly picked up from the basket is either an apple or an
orange is 13/40
(2)The probability of a fruit randomly picked up from the basket being an apple is 1/10 and that of
it being an orange is 9/40.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

3.In a basket there are only apples, oranges, and mangoes. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)The probability that a fruit randomly picked up from the basket is either an apple or a mango
is 31/40
(2)The probability of a fruit randomly picked up from the basket being either an orange or
a mango is 9/10
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

4.In a basket there are 4 apples, 9 oranges and remaining fruits are mangoes. If there are a total of 39 fruits in the basket, what is the probability that a fruit randomly picked up from the basket is a mango?
(A)4/39
(B)3/13
(C)1/3
(D)1/2
(E)2/3
Join the discussion
Source: — Data Sufficiency |

by Anurag@Gurome » Wed Jun 22, 2011 12:19 am
Question Number 1:
knight247 wrote:In a basket there are only apples, mangoes and oranges. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)There are 40 apples and 90 oranges.
(2)10% of the fruits are apples and 25% of the fruits are oranges.
To calculate the required probability we need to know the total number of fruits and the total number of mangoes in the basket or their ratio.

Statement 1: Not all the necessary information.

Not sufficient

Statement 2: (100 - 10 - 25) = 65% of the fruits are mangoes.
Hence, required probability = 65/100 = 13/20

Sufficient

The correct answer is B.
Anurag Mairal, Ph.D., MBA
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by Anurag@Gurome » Wed Jun 22, 2011 12:33 am
Question Number 2:
knight247 wrote:In a basket there are only apples, mangoes and oranges. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)The probability that a fruit randomly picked up from the basket is either an apple or an
orange is 13/40
(2)The probability of a fruit randomly picked up from the basket being an apple is 1/10 and that of
it being an orange is 9/40.
Note that, (Probability of a randomly picked fruit be apple + Probability of a randomly picked fruit be mango + Probability of a randomly picked fruit be orange) = 1

Statement 1: The probability that a fruit randomly picked up from the basket is either an apple or an orange = (Probability of a randomly picked fruit be apple) + (Probability of a randomly picked fruit be orange) = 1 - Probability of a randomly picked fruit be mango = 13/40

Probability of a randomly picked fruit be mango = 1 - 13/40 = 27/40

Sufficient

Statement 2: Probability of a randomly picked fruit be mango = 1 - (Probability of a randomly picked fruit be apple) + (Probability of a randomly picked fruit be orange) = 1 - 1/10 - 9/40 = 27/40

Sufficient

The correct answer is D.
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by Anurag@Gurome » Wed Jun 22, 2011 12:40 am
Question Number 3:
knight247 wrote:In a basket there are only apples, oranges, and mangoes. What is the probability that a fruit randomly picked up from the basket is a mango?
(1)The probability that a fruit randomly picked up from the basket is either an apple or a mango
is 31/40
(2)The probability of a fruit randomly picked up from the basket being either an orange or
a mango is 9/10
Probability of a randomly picked fruit be apple = P(apple) and same for others.

Statement 1: P(apple) + P(mango) = 31/40
We can't calculate P(mango) from this.

Not sufficient

Statement 2: P(orange) + P(mango) = 9/10
We can't calculate P(mango) from this.

Not sufficient

1 & 2 Together: [P(apple) + P(mango)] + [P(orange) + P(mango)] = 31/40 + 9/10 = 67/40 = 1 + 27/40
Now, P(apple) + P(mango) + P(orange) = 1

Hence, P(mango) = 27/40

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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by Anurag@Gurome » Wed Jun 22, 2011 12:41 am
Question Number 4:
knight247 wrote:In a basket there are 4 apples, 9 oranges and remaining fruits are mangoes. If there are a total of 39 fruits in the basket, what is the probability that a fruit randomly picked up from the basket is a mango?
P(mango) = Number of mangoes/Total number of fruits = (39 - 4 - 9)/39 = 26/39 = 2/3

The correct answer is E.
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by mirantdon » Tue Jun 28, 2011 1:43 am
b
d
c
e
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