Probability

Classical approach is used when events' outcomes are

• unequally likely

• equally likely

• Ambiguous

• For both unequally likely and equally likely

What is the probability of having 53 Mondays in a leap year? If the leap year is selected at random.

• 1/7

• 5/7

• 2/7

• None of them

Answer explanation

We are well aware that a leap year has 366 days.

Now, for 52 Mondays; 364 days are to be taken ∵ 52 x 7= 364 days

2 days are left out; sample space of possibilities can be expressed as following:

S= {MT, TW, W Th, Th F, F S, S Sun, Sun M}

P(Having 53 Mondays in leap year)= 2/7

Hence, probability is 2/7

A card is drawn from the set of 52 cards. Find the probability of getting a queen card.

• 1/13

• 1/26

• 1

• 1/52

What is the probability that a number selected from the numbers (1, 2, 3,..........,15) is a multiple of 4?

• 2/5

• 1/5

• 4/15

• 2/7

If three coins are tossed simultaneously, then the probability of getting at least two heads, is

• 1

• 3/2

• 1/2

• 5/7

Answer explanation

Possible outcomes of tossing three coins are:
(HHH), (HHT), (HTH), (THH), (TTT), (TTH), (THT),(HTT)

Here H and T are denoted for Head and Tail.
Total outcomes = 8

No. of outcomes with at least two heads = 4

P(of getting at most two heads)=4/8

Hence, probability required=1/2

100 cards are numbered from 1 to 100. Find the probability of getting a prime number.

• 0

• 1

• 2/11

• 1/4

A card is drawn at random from a well-shuffled pack of cards numbered 1 to 20. Find the probability of getting a number divisible by 3.

• 1/2

• 3/10

• 3/2

• 1/10

If a dice is thrown twice, find the probability of getting two 5's.

• 
  3/13

• 
  1/36

• 
  2/11

• 
  3/17

A card is drawn from a well shuffled pack of 52 cards. Find the probability of neither a heart nor a red king.

• 1/26

• 12/36

• 19/26

• 1/26

A die is cast twice and a coin is tossed twice. What is the probability that the die will turn a 6 each time and the coin will turn a tail every time?

• 1/112

• 1/144

• 2/11

• 1/141

Answer explanation

Each time the die is cast, it is an independent event. The probability of a getting a 6 is = 1/6. So the probability of getting a 6 when the die is cast twice = 1/6 × 1/6 = 1/36

Similarly the probability of getting a tail in two flips that follow each other (are independent) = (1/2) x (1/2) = 1/4

∴ As the two events i.e. casting the die and tossing the coin are independent, and the probability of both the events = (1/36) x (1/4)

Hence, the required value is 1/144.