Three coins are tossed 100 times, and three heads one head occurred 14 times and head did not occur 23 times. Find the probability of getting more than one head.
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Prove that `^100 C_2^(100)C_2+^(100)C_2^(100)C_4+^(100)C_4^(100)C_6++^(100)C_(98)^(100)C_(100)=1/2[^(200)C_(98)-^(100)C_(49)]dot`
To find `S = .^(100)C_(0).^(100)C_(2)+.^(100)C_(2).^(100)C_(4)+.^(100)C_(4).^(100)C_(6)+"....."+.^(100)C_(98).^(100)C_(100)` Consider, `.^(100)C_(0).^(100)C_(2)+.^(100)C_(1).^(100)C_(3) + .^(100)C_(2).^(100)C_(4)+.^(100)C_(3)+.^(100)C_(5)+"...." + .^(100)C_(98).^(100)C_(100)` `= .^(100)C_(0).^(100)C_(98)+.^(100)C_(1).^(100)C_(97) + .^(100)C_(2).^(100)C_(96)+.^(100)C_(3).^(100)C_(95) + "....."+^(100)C_(98) .^(100)C_(0)` = Coefficients of `x^(98)` in `(1+x)^(100) (1+x)^(100)` `= .^(200)C_(98) " "(1)` Also,...
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A coin is tossed three times, where (i) A : head on third toss,B: heads on first two tosses (ii) A: at least two heads, B : at most two heads (iii) A
If a coin is tossed three times, then the sample S is `S={HHH,HHT, HTH, HT T ,THH,THT, T TH, T T T }` `thereforen(S)=8.` (i) `A={HHH, HTH, THH, T TH]`...
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Three coins are tossed. If one of them shows tail, then find the probability that all three coins show tail.
Correct Answer - `1//7` Let E be the event which all three coins show tail and F be the event in which a coin shown tail. Therefor, `F={HHT}.` Hence, the required...
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A fair coin is tossed `n` times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value
Correct Answer - `n=14` According to question `""^(n)C_(6)((1)/(2))^(6)((1)/(2))^(n-6)=""^(n)C_(8)((1)/(2))^(8)((1)/(2))^(n-8)` `or ""^(n)C_(6)((1)/(2))^(n)=""^(n)C_(8)((1)/(2))^(n)` `or""^(n)C_(6)=""^(n)C_(8)=""^(n)C_(n-8)` `implies6=n-8orn=14`
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Two coins are tossed simultaneously. Find the probability of getting (i) exactly 1 head (ii) at most 1 head (iii) at least 1 head.
Correct Answer - (i) ` 1/2 (ii) 3/4 (iii) 3/4 `
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A piggy bank contains hundred 50p coins, fifty Rs. 1 coins, twenty ? 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will f
Correct Answer - `(i) 7/25 (ii) 22/25 (iii) 3/5`
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A die is thrown. Find the probability of (i) getting a 5 (ii) getting a 2 or a 3 (iii) getting an odd number (iv) getting a prime number (v) getting a
Correct Answer - `(i) 1/6 (ii) 1/3 (iii) 1/2 (iv) 1/2 (v) 1/3 (vi) 1/3`
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Three unbiased coins are tossed once. Find the probability of getting (i) exactly 2 tails (ii) exactly one tail (iii) at most 2 tails (iv) at least 2
Correct Answer - `(i) 3/8 (ii) 3/8 (iii) 7/8 (iv) 1/2 (v) 7/8`
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A coin is tossed 500 times and we get heads : 285 times and tails : 215 times When a coin is tossed at random , what is probability of getting (i) a h
Correct Answer - (i) 0.57 (ii) 0.43
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Two coins are tossed 400 times and we get two heads : 112 times, one head , 160 times , 0 head , 128 times . When two coins are tossed at random , wha
Correct Answer - (i) 0.28 (ii) 0.4 (iii) 0.32
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