Probability

During winters, on any given day, the probability of snowing in Kashmir is 1/3. In a given 3-day period, what is the probability that Kashmir experiences snowing?

• 1/3

• 1/27

• 19/27

• 26/27

• 1

Answer explanation

If Kashmir experiences snowing on any of the 3 days, we are done.

The question can be rephrased as "What is the probability that it snows at least on a single day in the 3-day period in Kashmir."

Use the complementary rule.

Probability of snowing at least one day = 1 - Probability of not snowing at all.

= 1 - (2/3)(2/3)(2/3) = 1 - (8/27) = 19/27.

If I toss a coin 5 times, what is the probability that I get at least 2 heads?

• 1/8

• 3/16

• 2/5

• 21/32

• 13/16

Answer explanation

Use the complementary rule.

Probability of at least 2 heads = 1 - Probability lesser than 2 heads.

Now, probability of no heads = Probability of 0 heads + Probabiity of 1 head.

The probability of event A taking place is 32% and the probability of event B taking place is 46%. If the probability of both the events happening is 12%, what is the probability that exactly only one of the events takes place?

Answer explanation

This is actually a Venn diagram question!

Probability of exactly one event happening = (Probability of A - Probability of both) + (Probability of B - Probability of both).

Given that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. What is the probability that event A occurs but not B?

• 0.24

• 0.06

• 0.3

• 0.5

• 0.2

Answer explanation

Note that both the events are independent.

Hence, you can get the probability of both of them by multiplying their individual probabilities.

Hence the required number = Probability of A * Probability of NOT B.

Probability of not B = 1 - Probability of B (complementary rule).

There are 13 pairs of socks in a closet. If I pick up two socks, what is the probability that they are not of the same pair? (Write your answer as a fraction, that is, m/n form)

Answer explanation

Probability of not being a pair = 1 - Probability of being a pair.

Probability of being a pair = (26/26) *(1/25)

Note that, the first sock can be anything. Depending on the first sock, the second sock should be picked such that they form a pair.

Hence, 1- (1/25) = 24/25.

There are two baskets full of footwears (includes sandals, flipflops and shoes) and there are 3 pairs of shoes in those two baskets.

First basket has 12 number of footwears (not pairs. Individual footwear pieces). The second basket has 25 individual footwear pieces.

First basket contains the left piece of the 3 pairs of shoes and the second basket contains the right piece of the 3 pairs.

If we select one footwear from the first basket and another footwear from the second basket, what is the probability that both the footwears selected will make a shoe pair? Write your answer in percentage.

Answer explanation

The probability of selecting a left shoe piece from the first basket is 3/12 = 1/4.

The probability of selecting the corresponding right piece from the second basket is 1/25.

Hence, (1/4)*(1/25) = 1/100.

Given: X and Y are independent events.

Quantity A: Probability of both occurring.

Quantity B: Probability of neither occurring.

• A

• B

• C

• D

Answer explanation

If P(A) = P(B) = 0.1, then P(AnB) = 0.01 and probability of neither is 1-0.01 = 0.99.

If P(A) = P(B) = 0.9, then P(AnB) = 0.81 and probability of neither is 1- 0.81 = 0.19.

Hence, D.

A coin is tossed 8 times. What is the probability that there is either a tail or head on each of the tosses?

Answer explanation

Clearly, either heads or tails will turn up when tossing a coin! This is a sure event! Hence the probability is 1.

I choose a random card from a deck of playing cards, place it back and again choose a random card.

What is the probability that both the cards were kings?

• 1/169

• 1/13

• 1/8

• 1/4

• 1/15

Answer explanation

Probability of a king = 4/13.

Even in the second draw, this probability does not change as we are replacing the first card in the deck.

Hence, (1/13)(1/13) = 1/169.

There is a pack of cards, numbered from 1 to 13, both inclusive. If I pick up two cards one after the other without replacement, what is the probability the product of the numbers in the cards is odd?

Write your answer as a fraction.