CLASS DISCUSSION - Probability

Question 1

A bag has 3 red balls, 4 blue balls and 5 green balls. When 3 balls are randomly picked (without replacement), what is the probability that exactly 2 of the balls have the same colour?

		$\dfrac{13}{44}$
		$\dfrac{15}{44}$
		$\dfrac{27}{44}$
		None of the above

Question 2

There is a coin toss for the two team captains at the start of every cricket match. The chances of Dhoni winning and losing a toss are equal. If Dhoni won the toss in his 8$^{th}$ match as captain, then what is the probability that this was the 4$^{th}$ coin toss that he had won?

		$\dfrac{1}{2}$
		$\dfrac{7}{32}$
		$\dfrac{35}{128}$
		$\dfrac{21}{256}$

Question 3

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.

Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?
[XAT 2015]

		0.004
		0.006
		0.216
		0.994
		0.996

Question 4

While travelling overseas, each of the players in the Indian cricket team is allowed to carry a maximum of 8 bats. Players are also allowed to travel without any bats (in which case they borrow another player's bat for a match). What is the probability that Sehwag and Dravid together carried at least 2 but not more than 10 bats in total?

		$\dfrac{2}{3}$
		$\dfrac{4}{9}$
		$\dfrac{7}{9}$
		$\dfrac{19}{27}$

Question 5

Sheetal and Tania play a game of Darts wherein the first person to hit the target wins the game. The probability of Sheetal and Tania hitting the target in a single throw is $\dfrac{3}{5}$ and $\dfrac{3}{4}$ respectively. Sheetal is to start the game with a throw, followed by a throw from Tania (if Sheetal misses the target). They continue to alternately throw till one of them hits the target. What is the probability of Tania winning the game?

		$\dfrac{1}{3}$
		$\dfrac{2}{3}$
		$\dfrac{4}{9}$
		$\dfrac{5}{9}$

Question 6

Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let $a$ denote the probability that at least one of the cards drawn is a king, and $b$ denote the probability of not drawing a king. The ratio of $a/b$ is
[XAT 2013]

		$\ge$ 0.25 and $\le$ 0.5
		$\ge$ 0.5 and $\le$ 0.75
		$\ge$ 0.75 and $\le$ 1.0
		$\ge$ 1.0 and $\le$ 1.25
		$\ge$ 1.25

Question 7

10 coins with distinct integers between 1 and 10 (both inclusive) stamped on them are distributed to Azma, Bala, Charlie, Delna and 6 others. The value of each coin is proportional to the integer on it.

What is the probability that Azma's coin has a higher value than Bala's coin, while Charlie's coin has a higher value than Delna's coin?

		$\dfrac{1}{4}$
		$\dfrac{1}{2}$
		$\dfrac{1}{3}$
		None of the above

Question 8

10 coins with distinct integers between 1 and 10 (both inclusive) stamped on them are distributed to Azma, Bala, Charlie, Delna and 6 others. The value of each coin is proportional to the integer on it.

What is the probability that Azma's coin has a higher value than those with Bala and Charlie, while Delna's coin has a higher value than Bala's coin?

		$\dfrac{1}{4}$
		$\dfrac{1}{6}$
		$\dfrac{5}{24}$
		$\dfrac{7}{24}$