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**Q.1. In a game, the entry fee is ₹5. The game consists of tossing a coin 3 times. If one or two heads show, Shweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she(i) loses the entry fee.(ii) gets double entry fee.(iii) just gets her entry fee.Ans. **Possible outcomes when a coin is tossed 3 times:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Total no. of outcomes = 8

(i) Shweta will lose the entry fee if she gets ‘TTT’.

∴ P(Shweta losses the entry fee) = 1/8

(ii) Shweta will get double the entry fee if she gets HHH,

∴ P(Shweta will get double the entry fee) = 1/8.

(iii) Shweta will get her entry fee, if she get HHH,

HTH, THH, TTH, THT or TTT

No. of ways = 6

∴ P(Shweta will get her entry fee) = 6/8 = 3/4.

The possible ways are (1, 2), (2, 1), (1, 3), (3, 1), (5, 1), (1, 5).

So, number of possible ways = 6

∴ Required probability = 6/36 = 1/6

So, total number of outcomes, n(S) = 36.

Number of outcomes for getting product 36,

n(E

∴ Probability for Apoorv getting the number

Also, Peehu throw one die.

So, total number of outcomes n(S) = 6

Number of outcomes for getting square of a number as 36.

n(E

∴ Probability for Peehu getting the number 36 =

Hence, Peehu has better chance of getting the number 36.

(i) the first player wins a prize?

(ii) the second player wins a prize, if the first has won?

Ans.

perfect square greater than 500 are 529,576,625,676, 729,784, 841,900, 961

∴ Probability of 1st player winning the prize = 9/1000

when 1st has won the prize then cards left = 999

(because card is not replaced)

Cards with no. which a perfect square greater than 500 = 8(1 winning number removed)

∴ Probability of second player wins a prize when the first player has won = 8/999.

Ans.

Let A = envelope contains no cash

Number of envelopes containing no cash = 1000 - (10 + 100 + 200) = 690

∴

Ans.

P (odd number) = 50/100 = 1/2

Ans.

Ans.

But P(not 1)

It means P(2, 3, 4, 5, 6) = 5/6

(i) How many different scores are possible?

(ii) What is the probability of getting a total of 7?

Ans.

Different total scores are 0,1, 6, 2, 7 or 12

Let A = getting a total of 7

No. of favourable outcomes are = 12

∴ P(A) = 12/36 = 1/3

(i) acceptable to Vamika?

(ii) acceptable to the trader?

Ans.

Let A = phone is good

Number of good phones = 42

∴

∴ Probability that Varnika will buy a phone = 7/8

Let B = Phone has no major defect number of Phones having no major defects = 48 - 3 = 45

∴ Probability that phone is acceptable to the trader = 15/16

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