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A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A.

1/2

B.

3/4

C.

3/8

D.

1/8

Answer with explanation

Answer: Option AExplanation

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Four cards are drawn at random from a pack of 52 cards. What is the probability of getting all four cards of the same suit?

A.

2860/27725

B.

2560/270725

C.

2360/270725

D.

2860/270725

Answer with explanation

Answer: Option DExplanation

Total No. Of cards =52

No.Of cards for each suit = 13

Total types Of French suit = 4(hearts,spades, diamonds,clubs)

Prob. = Conditional case /total case

For this conditional case of selecting all four same suit,it can be either hearts or spades or clubs or diamonds

So Total no. Of conditional case= no. of case of selecting all four cards of hearts suit +no.of case of selecting all four cards of spades suit +no.of case of selecting all four cards of clubs suit + no. of case of selecting all four cards of diamonds suit.

= 13C4+13C4+13C4+ 13C4

=4*(13C4)=2860

Total no. of case= 52C4=270725

So, probability of getting all four cards of the same suit=2860/270725

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In a charity show tickets numbered consecutively from 101 through 350 are placed in a box.

What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of 2?

A.

0.285

B.

0.40

C.

100/249

D.

99/250

Answer with explanation

Answer: Option BExplanation

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A speaks truth in 75% of cases and BB in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?

A.

35%

B.

5%

C.

15%

D.

65%

Answer with explanation

Answer: Option AExplanation

Different possible cases of contradiction,

AA speaks truth and BB does not speaks truth.

Or, AA does not speak truth and BB speaks truth.

=(3/4×1/5)+(1/4×4/5)=(3/4×1/5)+(1/4×4/5)

=3/20+4/20=3/20+4/20

=7/20=7/20

=35%

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In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?

A.

0.64

B.

0.68

C.

0.65

D.

0.67

Answer with explanation

Answer: Option DExplanation

P(M and S) = 0.40

P(M) = 0.60

P(S|M) = P(M and S)/P(S) = 0.40/0.60 = 2/3 = 0.67

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Consider the example of finding the probability of selecting a black card or a 6 from a deck of 52 cards.

A.

5/13

B.

7/15

C.

7/12

D.

7/13

Answer with explanation

Answer: Option DExplanation

We need to find out P(B or 6)

Probability of selecting a black card = 26/52

Probability of selecting a 6 = 4/52

Probability of selecting both a black card and a 6 = 2/52

P(B or 6) = P(B) + P(6) – P(B and 6)

= 26/52 + 4/52 – 2/52

= 28/52

= 7/13.

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