Lakshya Education MCQs

Question: State whether the given statement is true or false:

The probability of getting a multiple of 2 in a throw of an unbiased die is 12.
Options:
A.True
B.False
C.0.85
D.Cannot be determined
Answer: Option A
: A

There are 3 favourable outcomes out of a total of six outcomes in this case.
Multiples of 2 6 are 2, 4, and 6.
Hence, the probability is 12.

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Question 1. The probability of winning a game is 25, the probability of losing is__. (in decimal form)

: Winning or losing a game are complementary events. We know that, for complementary events, P(A) + P(notA) = 1.
Thus, if P(winning) = 25
Then, P(losing) = 1 - 25
P(losing) = 35 = 0.6.
Question 2. From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the  probability that number on the drawn card is a multiple of 3 or 7 ?
  1.    517
  2.    717
  3.    817
  4.    617
Answer: Option B
: B

The total number of possibleoutcomes(counting of the cards from 1to 17) = 17

Favourable outcomes are3, 6, 7, 9, 12, 14 and 15.
No. offavourable outcomes = 7

Let E be the event of getting a multiple of 3 or 7.
Probability P(E) = Number of outcomes favorable to ENumber of all possible outcomes of the experiment=717
Question 3. If P(A) and P(not A) are complementary events and P(A) =  0.15, then P(not A) = ?
  1.    0.35
  2.    0.3
  3.    0.85
  4.    Cannot be determined
Answer: Option C
: C

Given, P (A) = 0.15
As, P(A) and P(not A) are complementary events, P(A) + P(not A) = 1
P (not A) = 1 – P (A) = 1 – 0.15 = 0.85
Question 4. If three coins are tossed simultaneously, then the probability of getting at least one head and tail is _____.
  1.    14
  2.    12
  3.    34
  4.    23
Answer: Option C
: C

Given, a coin is tossed 3 times. Total possible outcomes= {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}(where H = Heads, T= Tails)
Total no. of possible outcomes = 8
Favourable outcomes (getting at least onehead and tail) = {HHT, HTT, HTH, THH, TTH, THT}
No. of favorable outcomes = 6
Probability of an event E,
P(E)=number of favourable outcomestotal number of outcomes P (getting at least onehead and tail) = 68 =34
The probability of getting at least onehead and a tail is34.
Question 5. In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.
  1.    15
  2.    125
  3.    1π
  4.    0
Answer: Option B
: B

Difference in radius between 2 circles = 4cm Let, radius of small circle be x.
x + 4 + 4 + 4 + 4 = 20 (from the diagram)
x = 4cm
Probability that the dart hits anywhere in the small circle = area(innermostcircle)area(outermostcircle) =π.42π202

=125
Question 6. There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.
  1.    1118
  2.    718
  3.    23
  4.    518
Answer: Option A
: A

Given,
Number of green balls = 5
Number of black balls = 6
Number of white balls = 7
Total numberof outcomes = 5 + 6+ 7 = 18
There are 18 balls out of which 11 are not white.
Number of favourable outcomes = 11

Probability of an event, P(E)=Number of favourable outcomesTotal number of outcomes
P(balldrawn isnotwhite) = 1118 Probability that the ball drawn is not white is 1118 . Alternate Method:
P (balldrawn is white) = 718
By complementary event formula,
P( balldrawn is white) +P( balldrawn is not white) = 1
P( balldrawn is not white)
=1P( balldrawn is white)
=1718=1118
Probability that the balldrawn is not white is 1118.

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